What is the integral of 5sin^5(x)cos(x) ?

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

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integral of 5sin^5(x)cos(x)

\int 5 sin^{5} (x) cos (x) d x

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

Solution steps

\int 5 sin^{5} (x) cos (x) d x

Take the constant out:

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

= 5 \cdot \int sin^{5} (x) cos (x) d x

Apply u-substitution

: \int u^{5} d u

= 5 \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

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

Substitute back

u = sin (x)

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

Simplify

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

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

Add a constant to the solution

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

x \to - 1 + lim (8 x^{2} + 5 m)

n = 1 \sum \infty (- 1)^{n + 1} \frac{2}{3 ^{n}}

x \to 6 lim (8)

\frac{d}{d θ} (cos (2 θ))

\int \frac{5 cos ^{2} ( x ) - 3 tan ( x )}{cos ( x )} d x

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