How do you integrate $int x^3cos(x^2)$ using integration by parts?

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Answer 1 · 2016-08-28T13:39:40

$= 1/2 x^2 sin(x^2) + 1/2cos(x^2) + C$

$int x^3cos(x^2)$

$int x^2 . x cos(x^2)$

$= int x^2 d/dx (1/2 sin(x^2))$

ready for IBP
$= 1/2 x^2 sin(x^2) - 1/2 int d/dx (x^2) sin(x^2)$

$= 1/2 x^2 sin(x^2) - int x sin(x^2)$

$= 1/2 x^2 sin(x^2) - int d/dx ( - 1/2cos(x^2))$

$= 1/2 x^2 sin(x^2) + 1/2cos(x^2) + C$

How do you integrate int x^3cos(x^2)int x^3cos(x^2) using integration by parts?