What is the integral of (3(x+5))/(sqrt(2x+15)) ?

The integral of (3(x+5))/(sqrt(2x+15)) is xsqrt(2x+15)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3(x+5))/(sqrt(2x+15))

\int \frac{3 ( x + 5 )}{2 x + 15} d x

x 2 x + 15 + C

Solution steps

\int \frac{3 ( x + 5 )}{2 x + 15} d x

Take the constant out:

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

= 3 \cdot \int \frac{x + 5}{2 x + 15} d x

Expand

\frac{x + 5}{2 x + 15} : \frac{x}{2 x + 15} + \frac{5}{2 x + 15}

= 3 \cdot \int \frac{x}{2 x + 15} + \frac{5}{2 x + 15} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 3 (\int \frac{x}{2 x + 15} d x + \int \frac{5}{2 x + 15} d x)

\int \frac{x}{2 x + 15} d x = \frac{1}{3} (x - 15) 2 x + 15

\int \frac{5}{2 x + 15} d x = 5 2 x + 15

= 3 (\frac{1}{3} (x - 15) 2 x + 15 + 5 2 x + 15)

Simplify

3 (\frac{1}{3} (x - 15) 2 x + 15 + 5 2 x + 15) : x 2 x + 15

= x 2 x + 15

Add a constant to the solution

= x 2 x + 15 + C

\int_{0}^{π} 6 sin (x) + sin (6 x) d x

x \to 4 + lim (\frac{6}{x - 4})

f (x) = x^{2} - 4 x - 5

\int (9 + x^{5})^{7} x^{4} d x

x \to 3 + lim (2 x^{2} - 4)

What is the integral of (3(x+5))/(sqrt(2x+15)) ?
The integral of (3(x+5))/(sqrt(2x+15)) is xsqrt(2x+15)+C