What is the integral of (1-3x)6x^5 ?

The integral of (1-3x)6x^5 is x^6-(18x^7)/7+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-3x)6x^5

\int (1 - 3 x) 6 x^{5} d x

x^{6} - \frac{18 x ^{7}}{7} + C

Solution steps

\int (1 - 3 x) \cdot 6 x^{5} d x

Take the constant out:

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

= 6 \cdot \int (1 - 3 x) x^{5} d x

Expand

(1 - 3 x) x^{5} : x^{5} - 3 x^{6}

= 6 \cdot \int x^{5} - 3 x^{6} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 3 x^{6} d x = \frac{3 x ^{7}}{7}

= 6 (\frac{x ^{6}}{6} - \frac{3 x ^{7}}{7})

Simplify

6 (\frac{x ^{6}}{6} - \frac{3 x ^{7}}{7}) : x^{6} - \frac{18 x ^{7}}{7}

= x^{6} - \frac{18 x ^{7}}{7}

Add a constant to the solution

= x^{6} - \frac{18 x ^{7}}{7} + C

\int (\frac{1}{4} x^{3} + 3 x^{2} - \frac{3}{5} x + 4) d x

\int - 9 x^{4} e^{x^{5}} d x

\int \frac{1}{( 1 + sin ( x ) + cos ( x ) )} d x

\frac{1}{2 x}

\int 8 x^{5} e^{x^{6}} d x

What is the integral of (1-3x)6x^5 ?
The integral of (1-3x)6x^5 is x^6-(18x^7)/7+C