What is the integral of 8*sin^4(x) ?

The integral of 8*sin^4(x) is -2sin^3(x)cos(x)+3x-3/2 sin(2x)+C

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integral of 8*sin^4(x)

\int 8 \cdot sin^{4} (x) d x

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

Solution steps

\int 8 sin^{4} (x) d x

Take the constant out:

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

= 8 \cdot \int sin^{4} (x) d x

Apply Integral Reduction

= 8 (- \frac{cos ( x ) sin ^{3} ( x )}{4} + \frac{3}{4} \cdot \int sin^{2} (x) d x)

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

= 8 (- \frac{cos ( x ) sin ^{3} ( x )}{4} + \frac{3}{4} \cdot \frac{1}{2} (x - \frac{1}{2} sin (2 x)))

Simplify

8 (- \frac{cos ( x ) sin ^{3} ( x )}{4} + \frac{3}{4} \cdot \frac{1}{2} (x - \frac{1}{2} sin (2 x))) : - 2 sin^{3} (x) cos (x) + 3 x - \frac{3}{2} sin (2 x)

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

Add a constant to the solution

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

d er i v a t i v e \frac{x ^{7}}{a} + \frac{a}{b} x^{6} - c x

l a pl a ce t r an s f or m cos (t - 1)

\int \frac{1}{x ^{2} - 324} d x

\frac{d}{d x} ((x^{2} - 6) e^{8 x})

\int 0 x d x

What is the integral of 8*sin^4(x) ?
The integral of 8*sin^4(x) is -2sin^3(x)cos(x)+3x-3/2 sin(2x)+C