What is the integral of (5x+3)^6 ?

The integral of (5x+3)^6 is 1/35 (5x+3)^7+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (5x+3)^6

\int (5 x + 3)^{6} d x

\frac{1}{35} (5 x + 3)^{7} + C

Solution steps

\int (5 x + 3)^{6} d x

Apply u-substitution

= \int \frac{u ^{6}}{5} d u

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{5} \cdot \frac{u ^{7}}{7}

Substitute back

u = 5 x + 3

= \frac{1}{5} \cdot \frac{( 5 x + 3 ) ^{7}}{7}

Simplify

\frac{1}{5} \cdot \frac{( 5 x + 3 ) ^{7}}{7} : \frac{1}{35} (5 x + 3)^{7}

= \frac{1}{35} (5 x + 3)^{7}

Add a constant to the solution

= \frac{1}{35} (5 x + 3)^{7} + C