What is the integral of y^2e^{xy^2}+1 ?

The integral of y^2e^{xy^2}+1 is x+e^{y^2x}+C

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integral of y^2e^{xy^2}+1

\int y^{2} e^{x y^{2}} + 1 d x

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

Solution steps

\int y^{2} e^{x y^{2}} + 1 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 1 d x + \int y^{2} e^{y^{2} x} d x

\int 1 d x = x

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

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

Add a constant to the solution

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

\int_{0}^{\frac{π}{2}} cos (4 x) d x

\frac{\partial}{\partial x} (2 + x^{2} + y^{2})

\frac{d}{d x} (\frac{- x ^{2} + 9}{( x ^{2} + 9 ) ^{2}})

x \to 3 lim (- x^{2} - 4 x + 8)

\frac{d}{d x} (3 x^{2} + 6 x + 6)

What is the integral of y^2e^{xy^2}+1 ?
The integral of y^2e^{xy^2}+1 is x+e^{y^2x}+C