What is the integral of (5-4x)^{12} ?

The integral of (5-4x)^{12} is 1/52 (-5+4x)^{13}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5-4x)^{12}

\int (5 - 4 x)^{12} d x

\frac{1}{52} (- 5 + 4 x)^{13} + C

Solution steps

\int (5 - 4 x)^{12} d x

Factor

5 - 4 x : - (- 5 + 4 x)

= \int (- (- 5 + 4 x))^{12} d x

Simplify

(- (- 5 + 4 x))^{12} : (- 5 + 4 x)^{12}

= \int (- 5 + 4 x)^{12} d x

Apply u-substitution

: \int \frac{u ^{12}}{4} d u

= \int \frac{u ^{12}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= \frac{1}{4} \cdot \frac{u ^{13}}{13}

Substitute back

u = - 5 + 4 x

= \frac{1}{4} \cdot \frac{( - 5 + 4 x ) ^{13}}{13}

Simplify

\frac{1}{4} \cdot \frac{( - 5 + 4 x ) ^{13}}{13} : \frac{1}{52} (- 5 + 4 x)^{13}

= \frac{1}{52} (- 5 + 4 x)^{13}

Add a constant to the solution

= \frac{1}{52} (- 5 + 4 x)^{13} + C

\int e^{x} sin (e^{x} + 7) d x

\int \frac{1}{x ln ( x ) ln ( x )} d x

\int 6 x (3 x^{2} + 7)^{4} d x

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

\int e^{18 x} (18) d x

What is the integral of (5-4x)^{12} ?
The integral of (5-4x)^{12} is 1/52 (-5+4x)^{13}+C