What is the integral of 6(1+6x)^4 ?

The integral of 6(1+6x)^4 is 1/5 (1+6x)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6(1+6x)^4

\int 6 (1 + 6 x)^{4} d x

\frac{1}{5} (1 + 6 x)^{5} + C

Solution steps

\int 6 (1 + 6 x)^{4} d x

Take the constant out:

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

= 6 \cdot \int (1 + 6 x)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{6} d u

= 6 \cdot \int \frac{u ^{4}}{6} d u

Take the constant out:

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

= 6 \cdot \frac{1}{6} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 6 \cdot \frac{1}{6} \cdot \frac{u ^{5}}{5}

Substitute back

u = 1 + 6 x

= 6 \cdot \frac{1}{6} \cdot \frac{( 1 + 6 x ) ^{5}}{5}

Simplify

6 \cdot \frac{1}{6} \cdot \frac{( 1 + 6 x ) ^{5}}{5} : \frac{1}{5} (1 + 6 x)^{5}

= \frac{1}{5} (1 + 6 x)^{5}

Add a constant to the solution

= \frac{1}{5} (1 + 6 x)^{5} + C

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

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

\int 2 x - e^{x} d x

\int x^{- \frac{7}{2}} d x

\int \frac{t - 4}{t} d t