What is the integral of xcos(2pix^2) ?

The integral of xcos(2pix^2) is 1/(4pi)sin(2pix^2)+C

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integral of xcos(2pix^2)

\int x cos (2 π x^{2}) d x

\frac{1}{4 π} sin (2 π x^{2}) + C

Solution steps

\int x cos (2 π x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{4 π} d u

= \int \frac{cos ( u )}{4 π} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4 π} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{4 π} sin (u)

Substitute back

u = 2 π x^{2}

= \frac{1}{4 π} sin (2 π x^{2})

Add a constant to the solution

= \frac{1}{4 π} sin (2 π x^{2}) + C

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What is the integral of xcos(2pix^2) ?
The integral of xcos(2pix^2) is 1/(4pi)sin(2pix^2)+C