What is the integral of sin(α)x ?

The integral of sin(α)x is 1/2 x^2sin(α)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(α)x

\int sin (α) x d x

\frac{1}{2} x^{2} sin (α) + C

Solution steps

\int sin (α) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sin (α) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin (α) \frac{x ^{2}}{2}

Simplify

sin (α) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} sin (α)

= \frac{1}{2} x^{2} sin (α)

Add a constant to the solution

= \frac{1}{2} x^{2} sin (α) + C

\int x^{2} \cdot cos (a x) d x

\int \frac{x ^{5} - 9 x ^{3} - 6 x ^{2} - 18}{x ^{3} - 9 x} d x

\int 81 + x^{2} d x

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

\int \frac{1}{3 y + 1} d y