What is the integral of-12xsin(6x^2+1) ?

The integral of-12xsin(6x^2+1) is cos(6x^2+1)+C

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integral of-12xsin(6x^2+1)

\int - 12 x sin (6 x^{2} + 1) d x

cos (6 x^{2} + 1) + C

Solution steps

\int - 12 x sin (6 x^{2} + 1) d x

Take the constant out:

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

= - 12 \cdot \int x sin (6 x^{2} + 1) d x

Apply u-substitution

: \int \frac{sin ( u )}{12} d u

= - 12 \cdot \int \frac{sin ( u )}{12} d u

Take the constant out:

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

= - 12 \cdot \frac{1}{12} \cdot \int sin (u) d u

Use the common integral:

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

= - 12 \cdot \frac{1}{12} (- cos (u))

Substitute back

u = 6 x^{2} + 1

= - 12 \cdot \frac{1}{12} (- cos (6 x^{2} + 1))

Simplify

- 12 \cdot \frac{1}{12} (- cos (6 x^{2} + 1)) : cos (6 x^{2} + 1)

= cos (6 x^{2} + 1)

Add a constant to the solution

= cos (6 x^{2} + 1) + C

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What is the integral of-12xsin(6x^2+1) ?
The integral of-12xsin(6x^2+1) is cos(6x^2+1)+C