What is the integral of sin(sqrt(1+2x)) ?

The integral of sin(sqrt(1+2x)) is -cos(sqrt(1+2x))sqrt(1+2x)+sin(sqrt(1+2x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(sqrt(1+2x))

\int sin (1 + 2 x) d x

- cos (1 + 2 x) 1 + 2 x + sin (1 + 2 x) + C

Solution steps

\int sin (1 + 2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Apply u-substitution

: \int sin (v) \cdot 2 v d v

= \frac{1}{2} \cdot \int sin (v) \cdot 2 v d v

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int sin (v) v d v

Apply Integration By Parts

: - v cos (v) - \int - cos (v) d v

= \frac{1}{2} \cdot 2 (- v cos (v) - \int - cos (v) d v)

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

= \frac{1}{2} \cdot 2 (- v cos (v) - (- sin (v)))

Substitute back

= \frac{1}{2} \cdot 2 (- 1 + 2 x cos (1 + 2 x) - (- sin (1 + 2 x)))

Simplify

\frac{1}{2} \cdot 2 (- 1 + 2 x cos (1 + 2 x) - (- sin (1 + 2 x))) : - cos (1 + 2 x) 1 + 2 x + sin (1 + 2 x)

= - cos (1 + 2 x) 1 + 2 x + sin (1 + 2 x)

Add a constant to the solution

= - cos (1 + 2 x) 1 + 2 x + sin (1 + 2 x) + C

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

\int cos (24 x) d x

\int 2 t + sec^{2} (t) d t

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

\int (1 + 2 x)^{3} d x

What is the integral of sin(sqrt(1+2x)) ?
The integral of sin(sqrt(1+2x)) is -cos(sqrt(1+2x))sqrt(1+2x)+sin(sqrt(1+2x))+C