We have to find the integration of
$$\int^{\infty}_{0}\frac{x}{1+x^4} dx$$
In this I am not getting any start.
Integration with infinity limits
2
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calculus
definite-integrals
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3$\frac{x}{1+(x^2)^2}$. Try substituion $t=x^2$. – 2017-01-05
2 Answers
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Set $x^2=t$, we have
$$\int^{\infty}_{0}\frac{x}{1+x^4} dx=\frac 12\int^{\infty}_{0}\frac{1}{1+t^2} dt=\frac {\pi}{4}$$
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Hint: Just substitute $u=x^2$ to give us $$I =\frac {1}{2}\int_{0}^{\infty}\frac {1}{1+u^2} du $$ giving us the answer as $$\boxed {\frac {\pi}{4}} $$ Hope it helps.