What is the integral of (4xy^2+3ysqrt(x)) ?

The integral of (4xy^2+3ysqrt(x)) is 2yx^{3/2}+2y^2x^2+C

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integral of (4xy^2+3ysqrt(x))

\int (4 x y^{2} + 3 y x) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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What is the integral of (4xy^2+3ysqrt(x)) ?
The integral of (4xy^2+3ysqrt(x)) is 2yx^{3/2}+2y^2x^2+C