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

n = 0 \sum \infty n! (x - 1)^{n}

\frac{d}{d x} (\frac{1}{x} + 2)

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

f (x) = x^{2} - 4 x + 3

\frac{d}{d x} (\frac{x ^{2} sin ( x )}{e ^{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