What is the integral of sin(x)-1/3 sin^3(x) ?

The integral of sin(x)-1/3 sin^3(x) is -2/3 cos(x)-1/9 cos^3(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)-1/3 sin^3(x)

\int sin (x) - \frac{1}{3} sin^{3} (x) d x

- \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x) + C

Solution steps

\int sin (x) - \frac{1}{3} sin^{3} (x) d x

Apply the Sum Rule:

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

= \int sin (x) d x - \int \frac{1}{3} sin^{3} (x) d x

\int sin (x) d x = - cos (x)

\int \frac{1}{3} sin^{3} (x) d x = \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})

= - cos (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})

Simplify

- cos (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3}) : - \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x)

= - \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x)

Add a constant to the solution

= - \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x) + C

\int 10 e^{- 30 t} sin (40 t) d t

\frac{d}{d x} (2 π \frac{x}{g ( x )})

y^{^{'}} - 2 y = x

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

\int_{0}^{5} (5 x^{2} - x^{3}) d x

What is the integral of sin(x)-1/3 sin^3(x) ?
The integral of sin(x)-1/3 sin^3(x) is -2/3 cos(x)-1/9 cos^3(x)+C