What is the integral of-18xsin(9x^2-7) ?

The integral of-18xsin(9x^2-7) is cos(9x^2-7)+C

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integral of-18xsin(9x^2-7)

\int - 18 x sin (9 x^{2} - 7) d x

cos (9 x^{2} - 7) + C

Solution steps

\int - 18 x sin (9 x^{2} - 7) d x

Take the constant out:

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

= - 18 \cdot \int x sin (9 x^{2} - 7) d x

Apply u-substitution

= - 18 \cdot \int \frac{sin ( 9 u - 7 )}{2} d u

Take the constant out:

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

= - 18 \cdot \frac{1}{2} \cdot \int sin (9 u - 7) d u

Apply u-substitution

= - 18 \cdot \frac{1}{2} \cdot \int sin (v) \frac{1}{9} d v

Take the constant out:

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

= - 18 \cdot \frac{1}{2} \cdot \frac{1}{9} \cdot \int sin (v) d v

Use the common integral:

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

= - 18 \cdot \frac{1}{2} \cdot \frac{1}{9} (- cos (v))

Substitute back

= - 18 \cdot \frac{1}{2} \cdot \frac{1}{9} (- cos (9 x^{2} - 7))

Simplify

- 18 \cdot \frac{1}{2} \cdot \frac{1}{9} (- cos (9 x^{2} - 7)) : cos (9 x^{2} - 7)

= cos (9 x^{2} - 7)

Add a constant to the solution

= cos (9 x^{2} - 7) + C

What is the integral of-18xsin(9x^2-7) ?
The integral of-18xsin(9x^2-7) is cos(9x^2-7)+C