What is the integral of 3xcos(1-x^2) ?

The integral of 3xcos(1-x^2) is -3/2 sin(1-x^2)+C

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integral of 3xcos(1-x^2)

\int 3 x cos (1 - x^{2}) d x

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

Solution steps

\int 3 x cos (1 - x^{2}) d x

Take the constant out:

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

= 3 \cdot \int x cos (1 - x^{2}) d x

Apply u-substitution

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

= 3 \cdot \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

= 3 (- \frac{1}{2} \cdot \int cos (u) d u)

Use the common integral:

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

= 3 (- \frac{1}{2} sin (u))

Substitute back

u = 1 - x^{2}

= 3 (- \frac{1}{2} sin (1 - x^{2}))

Simplify

3 (- \frac{1}{2} sin (1 - x^{2})) : - \frac{3}{2} sin (1 - x^{2})

= - \frac{3}{2} sin (1 - x^{2})

Add a constant to the solution

= - \frac{3}{2} sin (1 - x^{2}) + C

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What is the integral of 3xcos(1-x^2) ?
The integral of 3xcos(1-x^2) is -3/2 sin(1-x^2)+C