What is the integral of 3x^2(2x^2-5) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3x^2(2x^2-5)

\int 3 x^{2} (2 x^{2} - 5) d x

2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5} + C

Solution steps

\int 3 x^{2} (2 x^{2} - 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^{2} (2 x^{2} - 5) d x

Apply Integration By Parts

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

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

\int \frac{4 x ^{4}}{3} d x = \frac{4 x ^{5}}{15}

= 3 (\frac{1}{3} x^{3} (2 x^{2} - 5) - \frac{4 x ^{5}}{15})

Simplify

3 (\frac{1}{3} x^{3} (2 x^{2} - 5) - \frac{4 x ^{5}}{15}) : 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5}

= 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5}

Add a constant to the solution

= 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5} + C

\int (\frac{6}{x}) d x

\int 2 x + 6 e^{x} d x

\frac{d}{d x} (\frac{x}{x ^{2}})

y^{^{''}} - 2 y^{^{'}} + y = e^{x} ln (x)

\frac{d}{d x} (arcsin (\frac{x}{4}))

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