What is the integral of cos(x)(4+5sin^2(x)) ?

The integral of cos(x)(4+5sin^2(x)) is 4sin(x)+(5sin^3(x))/3+C

Popular >

integral of cos(x)(4+5sin^2(x))

\int cos (x) (4 + 5 sin^{2} (x)) d x

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

Solution steps

\int cos (x) (4 + 5 sin^{2} (x)) d x

Apply u-substitution

: \int 4 + 5 u^{2} d u

= \int 4 + 5 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 4 d u + \int 5 u^{2} d u

\int 4 d u = 4 u

\int 5 u^{2} d u = \frac{5 u ^{3}}{3}

= 4 u + \frac{5 u ^{3}}{3}

Substitute back

u = sin (x)

= 4 sin (x) + \frac{5 sin ^{3} ( x )}{3}

Add a constant to the solution

= 4 sin (x) + \frac{5 sin ^{3} ( x )}{3} + C

\frac{d}{d θ} (sin (2 θ))

\frac{( 3 s + 1 )}{s ^{2} + 4 s}

\int \frac{( x ^{3} - x ^{2} + 2 x - 6 )}{x} d x

- 2 x^{2} + 4 x - 4, at x = 3

y^{^{'}} - 7 y = 0

What is the integral of cos(x)(4+5sin^2(x)) ?
The integral of cos(x)(4+5sin^2(x)) is 4sin(x)+(5sin^3(x))/3+C