What is the integral of ((a+bx^7))/(sqrt(8ax+bx^8)) ?

The integral of ((a+bx^7))/(sqrt(8ax+bx^8)) is 1/4 sqrt(8ax+bx^8)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((a+bx^7))/(sqrt(8ax+bx^8))

\int \frac{( a + b x ^{7} )}{8 a x + b x ^{8}} d x

\frac{1}{4} 8 a x + b x^{8} + C

Solution steps

\int \frac{a + b x ^{7}}{8 a x + b x ^{8}} d x

Apply u-substitution

: \int \frac{1}{8 u} d u

= \int \frac{1}{8 u} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{8} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 8 a x + b x^{8}

= \frac{1}{8} \cdot 2 (8 a x + b x^{8})^{\frac{1}{2}}

Simplify

\frac{1}{8} \cdot 2 (8 a x + b x^{8})^{\frac{1}{2}} : \frac{1}{4} 8 a x + b x^{8}

= \frac{1}{4} 8 a x + b x^{8}

Add a constant to the solution

= \frac{1}{4} 8 a x + b x^{8} + C

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

\int cos (6 - 5 x) d x

\int x x + 4 d x

\int \frac{5}{x ^{2} - 25} d x

\int x 5 x + 8 d x

What is the integral of ((a+bx^7))/(sqrt(8ax+bx^8)) ?
The integral of ((a+bx^7))/(sqrt(8ax+bx^8)) is 1/4 sqrt(8ax+bx^8)+C