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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 7 sin (2 x) sin (x) d x = \frac{14}{3} sin^{3} (x)

= (2 + 7 sin^{2} (x)) sin (x) - \frac{14}{3} sin^{3} (x)

Simplify

(2 + 7 sin^{2} (x)) sin (x) - \frac{14}{3} sin^{3} (x) : 2 sin (x) + \frac{7}{3} sin^{3} (x)

= 2 sin (x) + \frac{7}{3} sin^{3} (x)

Add a constant to the solution

= 2 sin (x) + \frac{7}{3} sin^{3} (x) + C

x \to \infty lim (\frac{2 ^{x + 1} + 3 ^{x}}{2 ^{x} + 3 ^{x + 1}})

x \to 0 + lim (- ln (x))

\int \frac{y ^{2} + 1}{y + 1} d y

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + 1})

x 8 - x^{2}

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