What is the integral of \sqrt[3]{1+7x} ?

The integral of \sqrt[3]{1+7x} is 3/28 (1+7x)^{4/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of \sqrt[3]{1+7x}

\int 3 1 + 7 x d x

\frac{3}{28} (1 + 7 x)^{\frac{4}{3}} + C

Solution steps

\int 3 1 + 7 x d x

Apply u-substitution

: \int \frac{3 u}{7} d u

= \int \frac{3 u}{7} 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 3 u d u

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= \frac{1}{7} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = 1 + 7 x

= \frac{1}{7} \cdot \frac{3}{4} (1 + 7 x)^{\frac{4}{3}}

Simplify

\frac{1}{7} \cdot \frac{3}{4} (1 + 7 x)^{\frac{4}{3}} : \frac{3}{28} (1 + 7 x)^{\frac{4}{3}}

= \frac{3}{28} (1 + 7 x)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{28} (1 + 7 x)^{\frac{4}{3}} + C

\int \frac{8 - 2 x}{( x ^{2} - 8 x + 25 ) ^{2}} d x

\int 6 e^{- x} d x

\int x^{3} x^{2} - 4 d x

7 x^{6} - x^{e}

- 1

What is the integral of \sqrt[3]{1+7x} ?
The integral of \sqrt[3]{1+7x} is 3/28 (1+7x)^{4/3}+C