Hmm,in this problem i don't think substitution will work...what can i do?

Question

anonymous · Answer

$\huge\int\limits_{-\frac{ \pi }{ 2 }}^{\frac{ \pi }{ 2 }} \frac{ x^2 sinx }{ 1 + x^6 }$

perl · Answer

the integral of an odd function from -a to a is zero

anonymous · Answer

yes thank you ;) i didn't notice that

perl · Answer

sin x makes the whole function odd

perl · Answer

your welcome :)

anonymous · Answer

but it was as this:
$ \huge \int\frac{ x^2 sinx }{ 1 + x^6 } $

anonymous · Answer

how can i find this?

perl · Answer

that doesn't have a simple antiderivative

perl · Answer

the antiderivative cannot be expressed in terms of elementary functions (algebraic, trig, inverse trig, logs, exponential)

perl · Answer

"In calculus, every single-variable function composed of elementary functions has a derivative, but not every such function can be integrated, i.e., you cannot express the antiderivative in terms of elementary functions. Elementary functions include polynomials, rational functions, radical expressions, exponential functions, logarithms, trig functions, and inverse trig functions." http://calculus-geometry.hubpages.com/hub/List-of-Functions-You-Cannot-Integrate-No-Antiderivatives

perl · Answer

an example of a function which has no antiderivative is e^(x^2)

perl · Answer

but the function 
x*e^(x^2)  does have an antiderivative

perl · Answer

we can integrate x^2*sin(x) and x*sin(x), the problem is the denominator  1+ x^6

anonymous · Answer

well,thank you very much ;)