What is the integral of (3x+1)^{18} ?

The integral of (3x+1)^{18} is 1/57 (3x+1)^{19}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x+1)^{18}

\int (3 x + 1)^{18} d x

\frac{1}{57} (3 x + 1)^{19} + C

Solution steps

\int (3 x + 1)^{18} d x

Apply u-substitution

: \int \frac{u ^{18}}{3} d u

= \int \frac{u ^{18}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u^{18} d u

Apply the Power Rule

: \frac{u ^{19}}{19}

= \frac{1}{3} \cdot \frac{u ^{19}}{19}

Substitute back

u = 3 x + 1

= \frac{1}{3} \cdot \frac{( 3 x + 1 ) ^{19}}{19}

Simplify

\frac{1}{3} \cdot \frac{( 3 x + 1 ) ^{19}}{19} : \frac{1}{57} (3 x + 1)^{19}

= \frac{1}{57} (3 x + 1)^{19}

Add a constant to the solution

= \frac{1}{57} (3 x + 1)^{19} + C

\int \frac{3}{16 + x ^{2}} d x

\int \frac{cos ( 4 x )}{4} d x

\int (t - 1) d t

\int u (t) d t

\int 2 x^{2} (x - 2) (4 x - 5) d x

What is the integral of (3x+1)^{18} ?
The integral of (3x+1)^{18} is 1/57 (3x+1)^{19}+C