What is the integral of 6sin^4(x)cos(x) ?

The integral of 6sin^4(x)cos(x) is 6/5 sin^5(x)+C

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integral of 6sin^4(x)cos(x)

\int 6 sin^{4} (x) cos (x) d x

\frac{6}{5} sin^{5} (x) + C

Solution steps

\int 6 sin^{4} (x) cos (x) d x

Take the constant out:

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

= 6 \cdot \int sin^{4} (x) cos (x) d x

Apply u-substitution

: \int u^{4} d u

= 6 \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 6 \cdot \frac{u ^{5}}{5}

Substitute back

u = sin (x)

= 6 \cdot \frac{sin ^{5} ( x )}{5}

Simplify

6 \cdot \frac{sin ^{5} ( x )}{5} : \frac{6}{5} sin^{5} (x)

= \frac{6}{5} sin^{5} (x)

Add a constant to the solution

= \frac{6}{5} sin^{5} (x) + C

x^{3} d x + y^{3} d y = 0

\int sin^{5} (t) cos^{4} (t) d t

f^{^{'}} (x) = \frac{1 - x}{x ^{2}}

f (x) = \frac{2}{x + 4}, at x = - 3

\frac{d}{d x} (\frac{3}{x ^{2} - 2})

What is the integral of 6sin^4(x)cos(x) ?
The integral of 6sin^4(x)cos(x) is 6/5 sin^5(x)+C