What is the integral of (x^5)/(\sqrt[7]{ax^6+2)} ?

The integral of (x^5)/(\sqrt[7]{ax^6+2)} is (7(ax^6+2)^{6/7})/(36a)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^5)/(\sqrt[7]{ax^6+2)}

\frac{7 ( a x ^{6} + 2 ) ^{\frac{6}{7}}}{36 a} + C

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{7}{6} u^{\frac{6}{7}}

= \frac{1}{6 a} \cdot \frac{7}{6} u^{\frac{6}{7}}

Substitute back

u = a x^{6} + 2

= \frac{1}{6 a} \cdot \frac{7}{6} (a x^{6} + 2)^{\frac{6}{7}}

Simplify

\frac{1}{6 a} \cdot \frac{7}{6} (a x^{6} + 2)^{\frac{6}{7}} : \frac{7 ( a x ^{6} + 2 ) ^{\frac{6}{7}}}{36 a}

= \frac{7 ( a x ^{6} + 2 ) ^{\frac{6}{7}}}{36 a}

Add a constant to the solution

= \frac{7 ( a x ^{6} + 2 ) ^{\frac{6}{7}}}{36 a} + C

\int \frac{y - 8}{y ^{2} - y - 6} d y

\int cot (x) sin (x) d x

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

\int \frac{3 y}{2 y ^{2} + 5 y} d y

\int (x^{3} - 2 x + 1) sin (4 x) d x

What is the integral of (x^5)/(\sqrt[7]{ax^6+2)} ?
The integral of (x^5)/(\sqrt[7]{ax^6+2)} is (7(ax^6+2)^{6/7})/(36a)+C