What is the integral of xcos(1-x^2) ?

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

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integral of xcos(1-x^2)

\int x cos (1 - x^{2}) d x

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

Solution steps

\int x cos (1 - 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 = 1 - x^{2}

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

Add a constant to the solution

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

y = x^{12}

\int_{0}^{4} \frac{1}{x ^{2} + 9} d x

3 x - 2 x

\int e^{x} \cdot sin (x) d x

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{3} - 1})

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