What is the integral of xcos(x^4) ?

The integral of xcos(x^4) is (sqrt(pi))/(2sqrt(2))\C(sqrt(2/pi)sqrt(x^4))+C

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integral of xcos(x^4)

\int x cos (x^{4}) d x

\frac{π}{2 2} C (\frac{2}{π} x^{4}) + C

Solution steps

\int x cos (x^{4}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} cos (x^{4}) - \int - 2 x^{5} sin (x^{4}) d x

= \frac{1}{2} x^{2} cos (x^{4}) - \int - 2 x^{5} sin (x^{4}) d x

\int - 2 x^{5} sin (x^{4}) d x = - \frac{1}{2} (- x^{2} cos (x^{4}) + \frac{π}{2} C (\frac{2}{π} x^{4}))

= \frac{1}{2} x^{2} cos (x^{4}) - (- \frac{1}{2} (- x^{2} cos (x^{4}) + \frac{π}{2} C (\frac{2}{π} x^{4})))

Simplify

\frac{1}{2} x^{2} cos (x^{4}) - (- \frac{1}{2} (- x^{2} cos (x^{4}) + \frac{π}{2} C (\frac{2}{π} x^{4}))) : \frac{π}{2 2} C (\frac{2}{π} x^{4})

= \frac{π}{2 2} C (\frac{2}{π} x^{4})

Add a constant to the solution

= \frac{π}{2 2} C (\frac{2}{π} x^{4}) + C

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What is the integral of xcos(x^4) ?
The integral of xcos(x^4) is (sqrt(pi))/(2sqrt(2))\C(sqrt(2/pi)sqrt(x^4))+C