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

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

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integral of xcos(2-x^2)

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

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

Solution steps

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

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{n}{11 n ^{2} + 1}

\frac{\partial}{\partial x} (z ln ∣ x ∣)

(6 y + 2 t - 7) d t + (4 y + 6 t - 1) d y = 0, y (- 1) = 2

\frac{d y}{d x}, y = 3^{x}

\frac{d}{d x} (\frac{1}{x ^{\frac{3}{4}}})

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