What is the integral of cos(x)(2+5sin^2(x)) ?

The integral of cos(x)(2+5sin^2(x)) is 2sin(x)+5/3 sin^3(x)+C

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integral of cos(x)(2+5sin^2(x))

\int cos (x) (2 + 5 sin^{2} (x)) d x

2 sin (x) + \frac{5}{3} sin^{3} (x) + C

Solution steps

\int cos (x) (2 + 5 sin^{2} (x)) d x

Apply Integration By Parts

: (2 + 5 sin^{2} (x)) sin (x) - \int 5 sin (2 x) sin (x) d x

= (2 + 5 sin^{2} (x)) sin (x) - \int 5 sin (2 x) sin (x) d x

\int 5 sin (2 x) sin (x) d x = \frac{10}{3} sin^{3} (x)

= (2 + 5 sin^{2} (x)) sin (x) - \frac{10}{3} sin^{3} (x)

Simplify

(2 + 5 sin^{2} (x)) sin (x) - \frac{10}{3} sin^{3} (x) : 2 sin (x) + \frac{5}{3} sin^{3} (x)

= 2 sin (x) + \frac{5}{3} sin^{3} (x)

Add a constant to the solution

= 2 sin (x) + \frac{5}{3} sin^{3} (x) + C

\frac{\partial}{\partial x} (x^{4} ln (zy))

\frac{d}{d x} (\frac{e ^{x}}{x ^{n}})

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

\int \frac{7}{25 - x ^{2}} d x

2 x y

What is the integral of cos(x)(2+5sin^2(x)) ?
The integral of cos(x)(2+5sin^2(x)) is 2sin(x)+5/3 sin^3(x)+C