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

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

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integral of (2x^2+5x^3y)

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

2 x^{2} y + \frac{5 x ^{3} y ^{2}}{2} + C

Solution steps

\int 2 x^{2} + 5 x^{3} y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{2} d y + \int 5 x^{3} y d y

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

\int 5 x^{3} y d y = \frac{5 x ^{3} y ^{2}}{2}

= 2 x^{2} y + \frac{5 x ^{3} y ^{2}}{2}

Add a constant to the solution

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

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