What is the integral of (2xy^2-y^3) ?

The integral of (2xy^2-y^3) is -y^3x+y^2x^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2xy^2-y^3)

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

- y^{3} x + y^{2} x^{2} + C

Solution steps

\int 2 x y^{2} - y^{3} 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

= - \int y^{3} d x + \int 2 y^{2} x d x

\int y^{3} d x = y^{3} x

\int 2 y^{2} x d x = y^{2} x^{2}

= - y^{3} x + y^{2} x^{2}

Add a constant to the solution

= - y^{3} x + y^{2} x^{2} + C

\int 60 (1 + x^{2}) (7 + 15 x + 5 x^{3})^{12} d x

\int 10 e^{t} - t e^{t} + 1 d t

\int \frac{1}{( x + 9 ) ^{2}} d x

\int \frac{1}{1 - 25 t ^{2}} d t

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

What is the integral of (2xy^2-y^3) ?
The integral of (2xy^2-y^3) is -y^3x+y^2x^2+C