What is the integral of 3x^2+6xy^2 ?

The integral of 3x^2+6xy^2 is x^3+3y^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 3x^2+6xy^2

\int 3 x^{2} + 6 x y^{2} d x

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

Solution steps

\int 3 x^{2} + 6 x y^{2} 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 3 x^{2} d x + \int 6 y^{2} x d x

\int 3 x^{2} d x = x^{3}

\int 6 y^{2} x d x = 3 y^{2} x^{2}

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

Add a constant to the solution

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

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

\int 1 + \frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}} d x

\int (x^{2} - x (4 x - 2)) d x

\int \frac{8 x}{2 x + 7} d x

\int \frac{2 e ^{x}}{e ^{3 x} + 2 e ^{x}} d x

What is the integral of 3x^2+6xy^2 ?
The integral of 3x^2+6xy^2 is x^3+3y^2x^2+C