What is the integral of cos(x)(7+7sin^2(x)) ?

The integral of cos(x)(7+7sin^2(x)) is 7sin(x)+(7sin^3(x))/3+C

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integral of cos(x)(7+7sin^2(x))

\int cos (x) (7 + 7 sin^{2} (x)) d x

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

Solution steps

\int cos (x) (7 + 7 sin^{2} (x)) d x

Apply u-substitution

: \int 7 + 7 u^{2} d u

= \int 7 + 7 u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7 d u + \int 7 u^{2} d u

\int 7 d u = 7 u

\int 7 u^{2} d u = \frac{7 u ^{3}}{3}

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

f (x) = 6 sin^{6} (x)

\frac{\partial}{\partial t} (t^{8} e^{- x})

e^{x} (2 x + 2)

\int_{0}^{16} 8 x d x

k = 1 \sum \infty \frac{1}{1 + k ^{2}}

What is the integral of cos(x)(7+7sin^2(x)) ?
The integral of cos(x)(7+7sin^2(x)) is 7sin(x)+(7sin^3(x))/3+C