What is the integral of sin(4x) ?

The integral of sin(4x) is -1/4 cos(4x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(4x)

integral

sin (4 x)

- \frac{1}{4} cos (4 x) + C

Solution steps

\int sin (4 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{4} d u

= \int sin (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{4} (- cos (u))

Substitute back

u = 4 x

= \frac{1}{4} (- cos (4 x))

Simplify

= - \frac{1}{4} cos (4 x)

Add a constant to the solution

= - \frac{1}{4} cos (4 x) + C

\int \frac{1}{( 1 - 9 x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{1}{3} x^{5} d x

\int + 9 ln (x^{2} - 1) d x

\int \frac{x ^{3} + 4 x + 3}{x ^{2} + 2} d x

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