What is the integral of (3s)/(sqrt(1+s^2)) ?

The integral of (3s)/(sqrt(1+s^2)) is 3sqrt(1+s^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3s)/(sqrt(1+s^2))

\int \frac{3 s}{1 + s ^{2}} d s

3 1 + s^{2} + C

Solution steps

\int \frac{3 s}{1 + s ^{2}} d s

Take the constant out:

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

= 3 \cdot \int \frac{s}{1 + s ^{2}} d s

Apply u-substitution

: \int \frac{1}{2 u} d u

= 3 \cdot \int \frac{1}{2 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 3 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 1 + s^{2}

= 3 \cdot \frac{1}{2} \cdot 2 (1 + s^{2})^{\frac{1}{2}}

Simplify

3 \cdot \frac{1}{2} \cdot 2 (1 + s^{2})^{\frac{1}{2}} : 3 1 + s^{2}

= 3 1 + s^{2}

Add a constant to the solution

= 3 1 + s^{2} + C

\int (1 + 10 x - 5 y^{4}) d x

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

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

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

\int 5 x e^{0.005 x^{2}} d x

What is the integral of (3s)/(sqrt(1+s^2)) ?
The integral of (3s)/(sqrt(1+s^2)) is 3sqrt(1+s^2)+C