What is the integral of y^3+10xy^4-2x ?

The integral of y^3+10xy^4-2x is y^3x-x^2+5y^4x^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of y^3+10xy^4-2x

\int y^{3} + 10 x y^{4} - 2 x d x

y^{3} x - x^{2} + 5 y^{4} x^{2} + C

Solution steps

\int y^{3} + 10 x y^{4} - 2 x 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 x d x + \int 10 y^{4} x d x

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

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

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

= y^{3} x - x^{2} + 5 y^{4} x^{2}

Add a constant to the solution

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

What is the integral of y^3+10xy^4-2x ?
The integral of y^3+10xy^4-2x is y^3x-x^2+5y^4x^2+C