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

The integral of (2+y^2)e^y is e^yy^2-2e^yy+4e^y+C

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integral of (2+y^2)e^y

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

e^{y} y^{2} - 2 e^{y} y + 4 e^{y} + C

Solution steps

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

Apply Integration By Parts

= (2 + y^{2}) e^{y} - \int 2 y e^{y} d y

\int 2 y e^{y} d y = 2 (e^{y} y - e^{y})

= (2 + y^{2}) e^{y} - 2 (e^{y} y - e^{y})

Simplify

(2 + y^{2}) e^{y} - 2 (e^{y} y - e^{y}) : e^{y} y^{2} - 2 e^{y} y + 4 e^{y}

= e^{y} y^{2} - 2 e^{y} y + 4 e^{y}

Add a constant to the solution

= e^{y} y^{2} - 2 e^{y} y + 4 e^{y} + C

\int \frac{4 x}{x - 1} d x

\int e^{\frac{1}{x}} x^{- 2} d x

\int \frac{x ^{3} - 4 x ^{2} + 3}{x - 3} d x

\int (\frac{x ^{3} + 4 x ^{2} + 8 x + 5}{x ^{2} + 2 x + 1}) d x

\int \frac{1}{x ^{2} - 4} d x

What is the integral of (2+y^2)e^y ?
The integral of (2+y^2)e^y is e^yy^2-2e^yy+4e^y+C