How do you use Integration by Substitution to find $intx*sin(x^2)dx$ ?

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Answer 1 · 2014-09-26T09:19:31

Begin by letting making a u-substitution.

Let $u=x^2$

$du=2x dx$

$(du)/2=x dx =>$ This can be substituted in the original integral

$intx*sin(x^2)dx=intsin(u)*(du)/2=1/2intsin(u)du$

$=1/2[-cos(u)]+C$

$=-1/2[cos(u)]+C$

Rewrite in terms of $x$

$=-1/2[cos(x^2)]+C$

How do you use Integration by Substitution to find intx*sin(x^2)dxintx*sin(x^2)dx?