What is the integral of 3x^4(1-4x^5) ?

The integral of 3x^4(1-4x^5) is 3((x^5)/5-(2x^{10})/5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3x^4(1-4x^5)

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

3 (\frac{x ^{5}}{5} - \frac{2 x ^{10}}{5}) + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int x^{4} (1 - 4 x^{5}) d x

Expand

x^{4} (1 - 4 x^{5}) : x^{4} - 4 x^{9}

= 3 \cdot \int x^{4} - 4 x^{9} 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

= 3 (\int x^{4} d x - \int 4 x^{9} d x)

\int x^{4} d x = \frac{x ^{5}}{5}

\int 4 x^{9} d x = \frac{2 x ^{10}}{5}

= 3 (\frac{x ^{5}}{5} - \frac{2 x ^{10}}{5})

Add a constant to the solution

= 3 (\frac{x ^{5}}{5} - \frac{2 x ^{10}}{5}) + C

What is the integral of 3x^4(1-4x^5) ?
The integral of 3x^4(1-4x^5) is 3((x^5)/5-(2x^{10})/5)+C