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

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

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integral of 4xy^2+3x^2

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

y = cos (a^{8} + x^{8})

\frac{d}{d x} (2 csc^{2} (x) cot (x))

\frac{d}{d x} (\frac{4 x ^{\frac{2}{3}}}{x ^{2} + 1})

\int \frac{1}{( x + 1 ) x ^{2} + 2 x - 15} d x

x \to 3 + lim (\frac{2}{x ^{2} - 9})

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