What is the integral of x^2+8e^x+C ?

The integral of x^2+8e^x+C is (x^3)/3+8e^x+Cx+C

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integral of x^2+8e^x+C

\int x^{2} + 8 e^{x} + C d x

\frac{x ^{3}}{3} + 8 e^{x} + C x + C

Solution steps

\int x^{2} + 8 e^{x} + C 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 x^{2} d x + \int 8 e^{x} d x + \int C d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int 8 e^{x} d x = 8 e^{x}

\int C d x = C x

= \frac{x ^{3}}{3} + 8 e^{x} + C x

Add a constant to the solution

= \frac{x ^{3}}{3} + 8 e^{x} + C x + C

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{x} + e^{2 x}

\int \frac{1}{3 x + 2} d x

\int_{0}^{2} (x - 3)^{2} - (x - 1)^{2} d x

(x + 1) y^{^{'}} + x y = 0

\frac{d}{d x} (\frac{2 x ^{2} - 1}{3 x ^{3} - 1})

What is the integral of x^2+8e^x+C ?
The integral of x^2+8e^x+C is (x^3)/3+8e^x+Cx+C