What is the integral of (a+bx^6)/(sqrt(7ax+bx^7)) ?

The integral of (a+bx^6)/(sqrt(7ax+bx^7)) is 2/7 sqrt(7ax+bx^7)+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^6)/(sqrt(7ax+bx^7))

\int \frac{a + b x ^{6}}{7 a x + b x ^{7}} d x

\frac{2}{7} 7 a x + b x^{7} + C

Solution steps

\int \frac{a + b x ^{6}}{7 a x + b x ^{7}} d x

Apply u-substitution

: \int \frac{1}{7 u} d u

= \int \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{7} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 7 a x + b x^{7}

= \frac{1}{7} \cdot 2 (7 a x + b x^{7})^{\frac{1}{2}}

Simplify

\frac{1}{7} \cdot 2 (7 a x + b x^{7})^{\frac{1}{2}} : \frac{2}{7} 7 a x + b x^{7}

= \frac{2}{7} 7 a x + b x^{7}

Add a constant to the solution

= \frac{2}{7} 7 a x + b x^{7} + C

4 e^{- 5 t} - 3 e^{- t}

\frac{d y}{d t} + y = sin (t)

t sin (3 t) - 2 t cos (t)

2 sin (x^{2})

\int 2 sec^{2} (x) tan (x) d x

What is the integral of (a+bx^6)/(sqrt(7ax+bx^7)) ?
The integral of (a+bx^6)/(sqrt(7ax+bx^7)) is 2/7 sqrt(7ax+bx^7)+C