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

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

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integral of (xcos(x^2))

\int (x cos (x^{2})) d x

\frac{1}{2} sin (x^{2}) + C

Solution steps

\int x cos (x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = x^{2}

= \frac{1}{2} sin (x^{2})

Add a constant to the solution

= \frac{1}{2} sin (x^{2}) + C

\int (- x^{2} + 4) d x

y^{^{'}} = y cos (2 x)

\int_{1}^{\infty} x e^{- x^{2}} d x

y (2 x y + 1) d x - x d y = 0

sin (3 x) + cos (3 x)

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