What is the integral of (6x^2y+2x) ?

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

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integral of (6x^2y+2x)

\int (6 x^{2} y + 2 x) d y

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

Solution steps

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

\int 2 x d y = 2 x y

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

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

Add a constant to the solution

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

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

\int \frac{sec ^{2} ( x )}{tan ^{7} ( x )} d x

\int csc (x) sec (x) d x

f (x) = 6 x

f (x) = 3 e^{(2 x^{2})}

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