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

The integral of xsin(1-x^2) is 1/2 cos(1-x^2)+C

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integral of xsin(1-x^2)

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{sin ( u )}{2} d u

= \int - \frac{sin ( 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 sin (u) d u

Use the common integral:

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

= - \frac{1}{2} (- cos (u))

Substitute back

u = 1 - x^{2}

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

Simplify

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

Add a constant to the solution

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

\int \frac{7 arcsin ( x )}{x ^{2}} d x

\frac{d y}{d x} = 5 x (y - 1)^{\frac{1}{5}}

- 2 x^{5} + 11 x^{3}

\frac{d}{d x} ((3 - x) (2 - x) (5 - x))

\int (3 x - 2) e^{x} d x

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