What is the integral of 8sin(2)(x)cos(3)(x) ?

The integral of 8sin(2)(x)cos(3)(x) is 8/3 sin(2)cos(3)x^3+C

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integral of 8sin(2)(x)cos(3)(x)

\int 8 sin (2) (x) cos (3) (x) d x

\frac{8}{3} sin (2) cos (3) x^{3} + C

Solution steps

\int 8 sin (2) x cos (3) x d x

Take the constant out:

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

= 8 sin (2) cos (3) \cdot \int xx d x

Simplify

xx : x^{2}

= 8 sin (2) cos (3) \cdot \int x^{2} d x

Apply the Power Rule

= 8 sin (2) cos (3) \frac{x ^{3}}{3}

Simplify

8 sin (2) cos (3) \frac{x ^{3}}{3} : \frac{8}{3} sin (2) cos (3) x^{3}

= \frac{8}{3} sin (2) cos (3) x^{3}

Add a constant to the solution

= \frac{8}{3} sin (2) cos (3) x^{3} + C

What is the integral of 8sin(2)(x)cos(3)(x) ?
The integral of 8sin(2)(x)cos(3)(x) is 8/3 sin(2)cos(3)x^3+C