What is the integral of 7sin^3(x)cos(x) ?

The integral of 7sin^3(x)cos(x) is 7/4 sin^4(x)+C

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integral of 7sin^3(x)cos(x)

\int 7 sin^{3} (x) cos (x) d x

\frac{7}{4} sin^{4} (x) + C

Solution steps

\int 7 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

= 7 \cdot \int sin^{3} (x) cos (x) d x

Apply u-substitution

: \int u^{3} d u

= 7 \cdot \int u^{3} d u

Apply the Power Rule

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

= 7 \cdot \frac{u ^{4}}{4}

Substitute back

u = sin (x)

= 7 \cdot \frac{sin ^{4} ( x )}{4}

Simplify

7 \cdot \frac{sin ^{4} ( x )}{4} : \frac{7}{4} sin^{4} (x)

= \frac{7}{4} sin^{4} (x)

Add a constant to the solution

= \frac{7}{4} sin^{4} (x) + C

\frac{d}{d x} (\frac{1}{6} ln (e^{2 x} - e^{x} + 1))

x h (x)

\frac{1}{s ^{2} ( s ^{2} + 2 ^{2} )}

y^{^{'}} + 6 x y = 0

f (x) = (4 x^{2} - 6 x) e^{x}

What is the integral of 7sin^3(x)cos(x) ?
The integral of 7sin^3(x)cos(x) is 7/4 sin^4(x)+C