What is the integral of 3sin^6(x)cos(x) ?

The integral of 3sin^6(x)cos(x) is 3/7 sin^7(x)+C

Popular >

integral of 3sin^6(x)cos(x)

\int 3 sin^{6} (x) cos (x) d x

\frac{3}{7} sin^{7} (x) + C

Solution steps

\int 3 sin^{6} (x) cos (x) d x

Take the constant out:

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

= 3 \cdot \int sin^{6} (x) cos (x) d x

Apply u-substitution

: \int u^{6} d u

= 3 \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= 3 \cdot \frac{u ^{7}}{7}

Substitute back

u = sin (x)

= 3 \cdot \frac{sin ^{7} ( x )}{7}

Simplify

3 \cdot \frac{sin ^{7} ( x )}{7} : \frac{3}{7} sin^{7} (x)

= \frac{3}{7} sin^{7} (x)

Add a constant to the solution

= \frac{3}{7} sin^{7} (x) + C

x \to 0 lim (100)

\frac{d}{d x} (a x^{2} e^{2 x})

h (t) = (t^{\frac{2}{5}} + 3) (3 t^{5} + 5)

x \to + 8 - lim (\frac{x}{x - 8})

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

What is the integral of 3sin^6(x)cos(x) ?
The integral of 3sin^6(x)cos(x) is 3/7 sin^7(x)+C