Mixing
very nasty Integral
Clash Royale CLAN TAG#URR8PPP
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I am looking for a way to deal with concatinations of functions when integrating.
in particular i am trying to integrate the following
$$int_0^t f(g(h(x)))dx$$ for $$f(x)=x^2;;;;;; g(x)=x-x_*;;;;;;h(x)=fracexp(ax)x_01+fracba(exp(ax)-1)x_0$$
Does anyone have any tips? i keep trying substitution but that does not help and i also have a hard time looking for a logarithmic integration ($h$ could be rewritten via a logarithmic term). Can anyon give tips? I don't see any way to apply complex analysis either.
for clearance:
$int_0^t left(fracexp(ax)x_01+fracba(exp(ax)-1)x_0 -x_*right)^2 dx$
real-analysis complex-analysis
asked Aug 2 at 12:12
Danny
194
add a comment |Â
up vote
0
down vote
favorite
I am looking for a way to deal with concatinations of functions when integrating.
in particular i am trying to integrate the following
$$int_0^t f(g(h(x)))dx$$ for $$f(x)=x^2;;;;;; g(x)=x-x_*;;;;;;h(x)=fracexp(ax)x_01+fracba(exp(ax)-1)x_0$$
Does anyone have any tips? i keep trying substitution but that does not help and i also have a hard time looking for a logarithmic integration ($h$ could be rewritten via a logarithmic term). Can anyon give tips? I don't see any way to apply complex analysis either.
for clearance:
$int_0^t left(fracexp(ax)x_01+fracba(exp(ax)-1)x_0 -x_*right)^2 dx$
real-analysis complex-analysis
asked Aug 2 at 12:12
Danny
194
$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
2
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
1
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
1
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am looking for a way to deal with concatinations of functions when integrating.
in particular i am trying to integrate the following
$$int_0^t f(g(h(x)))dx$$ for $$f(x)=x^2;;;;;; g(x)=x-x_*;;;;;;h(x)=fracexp(ax)x_01+fracba(exp(ax)-1)x_0$$
Does anyone have any tips? i keep trying substitution but that does not help and i also have a hard time looking for a logarithmic integration ($h$ could be rewritten via a logarithmic term). Can anyon give tips? I don't see any way to apply complex analysis either.
for clearance:
$int_0^t left(fracexp(ax)x_01+fracba(exp(ax)-1)x_0 -x_*right)^2 dx$
real-analysis complex-analysis
asked Aug 2 at 12:12
Danny
194
I am looking for a way to deal with concatinations of functions when integrating.
in particular i am trying to integrate the following
$$int_0^t f(g(h(x)))dx$$ for $$f(x)=x^2;;;;;; g(x)=x-x_*;;;;;;h(x)=fracexp(ax)x_01+fracba(exp(ax)-1)x_0$$
Does anyone have any tips? i keep trying substitution but that does not help and i also have a hard time looking for a logarithmic integration ($h$ could be rewritten via a logarithmic term). Can anyon give tips? I don't see any way to apply complex analysis either.
for clearance:
$int_0^t left(fracexp(ax)x_01+fracba(exp(ax)-1)x_0 -x_*right)^2 dx$
real-analysis complex-analysis
asked Aug 2 at 12:12
Danny
194
edited Aug 3 at 8:18
asked Aug 2 at 12:12
Danny
194
asked Aug 2 at 12:12
Danny
194
asked Aug 2 at 12:12
Danny
194
194
$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
2
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
1
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
1
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47
add a comment |Â
$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
2
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
1
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
1
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47
$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
2
2
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
1
1
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
1
1
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47
add a comment |Â
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$$mathcalI_spacetextaleft(textb,x_0,x_*right):=int_0^tfracx_0cdotexpleft(textacdotleft(x-x_*right)^2right)1+x_0cdotfractextbtextacdotleft(expleft(textacdotleft(x-x_*right)^2right)-1right)spacetextdttag1$$
– Jan
Aug 2 at 12:21
2
@Jan I think that is $int_0^th(f(g(x))) dx$
– Aweygan
Aug 2 at 12:49
Why are you trying to integrate this?
– user223391
Aug 2 at 13:13
1
i want to integrate this in order to get a stabilty property for a nonlinear stochastic filter process. sadly the integral looks like this.
– Danny
Aug 3 at 8:10
1
There is no formula to compute $int f(g(t));dt$ in terms of $int g(t);dt$ and $int f(t);dt$. In fact, there is no formula for $int f(t)^2;dt$ in terms of $int f(t);dt$.
– GEdgar
Aug 3 at 11:47