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

f (x) = 4 e^{x} + x, at x = 0

\frac{d}{d x} (cos (\frac{1 - e ^{7 x}}{1 + e ^{7 x}}))

f (x) = \frac{csc ( x )}{1 + csc ( x )}

f (x) = x^{2} \cdot e^{x}

\int_{1}^{4} 4 x^{2} 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