What is the integral of cos(x)(2+sin(x))^3 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(x)(2+sin(x))^3

\int cos (x) (2 + sin (x))^{3} d x

\frac{( 2 + sin ( x ) ) ^{4}}{4} + C

Solution steps

\int cos (x) (2 + sin (x))^{3} d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

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

Substitute back

u = 2 + sin (x)

= \frac{( 2 + sin ( x ) ) ^{4}}{4}

Add a constant to the solution

= \frac{( 2 + sin ( x ) ) ^{4}}{4} + C

\int e^{- 2 a t} d t

\int \frac{tan ( x )}{cos ( 2 x )} d x

\int \frac{( x - 4 )}{x ^{2}} d x

\int e^{- 3 x} x^{2} d x

\int x e^{2 x - 1} d x

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