What is the integral of (3+e^x(y^2+3y+2)) ?

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

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integral of (3+e^x(y^2+3y+2))

\int (3 + e^{x} (y^{2} + 3 y + 2)) d x

3 x + (2 + y^{2} + 3 y) e^{x} + C

Solution steps

\int 3 + e^{x} (y^{2} + 3 y + 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 d x + \int (2 + y^{2} + 3 y) e^{x} d x

\int 3 d x = 3 x

\int (2 + y^{2} + 3 y) e^{x} d x = (2 + y^{2} + 3 y) e^{x}

= 3 x + (2 + y^{2} + 3 y) e^{x}

Add a constant to the solution

= 3 x + (2 + y^{2} + 3 y) e^{x} + C

\frac{\partial}{\partial x} (\frac{y}{( x + z )})

\int 4 x^{2} + 5 x - 3 d x

y = \frac{10}{1 + e ^{- x}}, (0, 5)

(3 x^{3} + 3) (x^{4} - 3 x)

\int_{0}^{5} x e^{- 4 x} d x

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