What is the integral of 45sin(3)(x)cos(2)(x) ?

The integral of 45sin(3)(x)cos(2)(x) is 15sin(3)cos(2)x^3+C

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integral of 45sin(3)(x)cos(2)(x)

\int 45 sin (3) (x) cos (2) (x) d x

15 sin (3) cos (2) x^{3} + C

Solution steps

\int 45 sin (3) x cos (2) x d x

Take the constant out:

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

= 45 sin (3) cos (2) \cdot \int xx d x

Simplify

xx : x^{2}

= 45 sin (3) cos (2) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= 45 sin (3) cos (2) \frac{x ^{3}}{3}

Simplify

45 sin (3) cos (2) \frac{x ^{3}}{3} : 15 sin (3) cos (2) x^{3}

= 15 sin (3) cos (2) x^{3}

Add a constant to the solution

= 15 sin (3) cos (2) x^{3} + C

x^{3}

x \to 1 + lim (e^{x})

x^{\frac{4}{7}}

x \to 3 lim ((x) + 3 x)

6 cos (t - 2)

What is the integral of 45sin(3)(x)cos(2)(x) ?
The integral of 45sin(3)(x)cos(2)(x) is 15sin(3)cos(2)x^3+C