What is the integral of 4sin^3(x)cos(x) ?

The integral of 4sin^3(x)cos(x) is sin^4(x)+C

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integral of 4sin^3(x)cos(x)

\int 4 sin^{3} (x) cos (x) d x

sin^{4} (x) + C

Solution steps

\int 4 sin^{3} (x) cos (x) d x

Take the constant out:

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

= 4 \cdot \int sin^{3} (x) cos (x) d x

Apply u-substitution

: \int u^{3} d u

= 4 \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= 4 \cdot \frac{u ^{4}}{4}

Substitute back

u = sin (x)

= 4 \cdot \frac{sin ^{4} ( x )}{4}

Simplify

4 \cdot \frac{sin ^{4} ( x )}{4} : sin^{4} (x)

= sin^{4} (x)

Add a constant to the solution

= sin^{4} (x) + C

\int \frac{1}{( x ^{2} - 4 ) ^{(\frac{3}{2})}} d x

\frac{x - 1}{x + 1}

\frac{d}{d x} (e^{x} (x - 5))

2 e^{z}

\frac{d}{d x} (\frac{3 x - 7}{2 x + 4})

What is the integral of 4sin^3(x)cos(x) ?
The integral of 4sin^3(x)cos(x) is sin^4(x)+C