What is the integral of ln(y)+2xe^{x^2} ?

The integral of ln(y)+2xe^{x^2} is ln(y)x+e^{x^2}+C

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integral of ln(y)+2xe^{x^2}

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

ln (y) x + e^{x^{2}} + C

Solution steps

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

\int ln (y) d x = ln (y) x

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

= ln (y) x + e^{x^{2}}

Add a constant to the solution

= ln (y) x + e^{x^{2}} + C

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What is the integral of ln(y)+2xe^{x^2} ?
The integral of ln(y)+2xe^{x^2} is ln(y)x+e^{x^2}+C