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

Take the constant out:

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

= - \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

\frac{d}{d θ} (cos (2 θ))

(x^{2} + 1) (\frac{d y}{d x}) + x y - x = 0

\frac{d}{d x} (\frac{1}{3} \cdot x^{3})

f (x) = e^{\frac{x}{( x - 9 )}}

\frac{d}{d s} (\frac{2 s ^{2}}{( s - 6 ) ^{3}})

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