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

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

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integral of xcos(pix^2)

\int x cos (π x^{2}) d x

\frac{1}{2 π} sin (π x^{2}) + C

Solution steps

\int x cos (π x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{2 π} d u

= \int \frac{cos ( u )}{2 π} d u

Take the constant out:

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

= \frac{1}{2 π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2 π} sin (u)

Substitute back

u = π x^{2}

= \frac{1}{2 π} sin (π x^{2})

Add a constant to the solution

= \frac{1}{2 π} sin (π x^{2}) + C

x y^{^{'}} - y = 0

\frac{3 + ( \frac{4}{s} )}{s + 5}

\frac{d}{d x} (x + x y)

n = 1 \sum \infty \frac{5}{n + 1}

\int_{0}^{1} (3 t - 1)^{50} d t

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