What is the integral of sin(5x+1) ?

The integral of sin(5x+1) is -1/5 cos(5x+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(5x+1)

\int sin (5 x + 1) d x

- \frac{1}{5} cos (5 x + 1) + C

Solution steps

\int sin (5 x + 1) d x

Apply u-substitution

: \int sin (u) \frac{1}{5} d u

= \int sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{5} (- cos (u))

Substitute back

u = 5 x + 1

= \frac{1}{5} (- cos (5 x + 1))

Simplify

= - \frac{1}{5} cos (5 x + 1)

Add a constant to the solution

= - \frac{1}{5} cos (5 x + 1) + C

\int \frac{1}{cos ( x ) ( 1 + sin ( x ) )} d x

\int e^{3 x - 7} d x

\int ln (2^{x}) d x

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

\int \frac{x}{6 - x} d x

What is the integral of sin(5x+1) ?
The integral of sin(5x+1) is -1/5 cos(5x+1)+C