Mathematics

# Integrate with respect to $x$:$x\sin x^2$.

$\dfrac{-\cos^2x}{2}+C$

##### SOLUTION

Consider the given integral.

$I=\int{x\sin {{x}^{2}}dx}$

Let,

$t={{x}^{2}}\Rightarrow xdx=\dfrac{dt}{2}$

Therefore,

$I=\int{x\sin {{x}^{2}}dx}$

$I=\dfrac{1}{2}\int{\sin tdt}$

$I=-\dfrac{1}{2}\cos t+C$

$I=-\dfrac{1}{2}\cos \left( {{x}^{2}} \right)+C$

Hence, this is the required result.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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