What is the integral of x^2+5e^x+C ?

The integral of x^2+5e^x+C is (x^3)/3+5e^x+Cx+C

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integral of x^2+5e^x+C

\int x^{2} + 5 e^{x} + C d x

\frac{x ^{3}}{3} + 5 e^{x} + C x + C

Solution steps

\int x^{2} + 5 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 5 e^{x} d x + \int C d x

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

\int 5 e^{x} d x = 5 e^{x}

\int C d x = C x

= \frac{x ^{3}}{3} + 5 e^{x} + C x

Add a constant to the solution

= \frac{x ^{3}}{3} + 5 e^{x} + C x + C

\int_{0}^{1} (10 + x x) d x

\frac{4 s e ^{- 4 s}}{3 s ^{2} + 27}

\int [x ln (x^{2} + 1)] d x

y^{^{''}} + y = sin (t), y (0) = 0, y^{^{'}} (0) = 0

x y y^{^{'}} = x^{2} e^{\frac{y}{x}} + y^{2}

What is the integral of x^2+5e^x+C ?
The integral of x^2+5e^x+C is (x^3)/3+5e^x+Cx+C