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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2(3x-5)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Expand

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

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

Add a constant to the solution

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

\int 1 + cot^{2} (5 x) d x

\int \frac{x + arctan ( x )}{1 + x ^{2}} d x

\int - 9 e^{x} d x

\int (t + 1) d t

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