What is the integral of (4+5x)^5 ?

The integral of (4+5x)^5 is 1/30 (4+5x)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (4+5x)^5

\int (4 + 5 x)^{5} d x

\frac{1}{30} (4 + 5 x)^{6} + C

Solution steps

\int (4 + 5 x)^{5} d x

Apply u-substitution

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

Apply the Power Rule

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

Substitute back

u = 4 + 5 x

= \frac{1}{5} \cdot \frac{( 4 + 5 x ) ^{6}}{6}

Simplify

\frac{1}{5} \cdot \frac{( 4 + 5 x ) ^{6}}{6} : \frac{1}{30} (4 + 5 x)^{6}

= \frac{1}{30} (4 + 5 x)^{6}

Add a constant to the solution

= \frac{1}{30} (4 + 5 x)^{6} + C

\int \frac{x}{x + 1} d x

\int \frac{6 x + 8}{x ( x + 2 ) ^{2}} d x

\int 9 cos (π x) d x

\int e^{r} r d r

\int \frac{5 x - 2}{x ^{2} - 2 x} d x