What is the integral of x^2+6e^x+C ?

The integral of x^2+6e^x+C is (x^3)/3+6e^x+Cx+C

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integral of x^2+6e^x+C

\int x^{2} + 6 e^{x} + C d x

\frac{x ^{3}}{3} + 6 e^{x} + C x + C

Solution steps

\int x^{2} + 6 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 6 e^{x} d x + \int C d x

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

\int 6 e^{x} d x = 6 e^{x}

\int C d x = C x

= \frac{x ^{3}}{3} + 6 e^{x} + C x

Add a constant to the solution

= \frac{x ^{3}}{3} + 6 e^{x} + C x + C

\int e x d x

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

y^{^{''}} - y = \frac{e ^{x}}{e ^{x}}

\int_{1}^{2} 4 - x^{2} d x

\frac{d}{d x} (arctan (sin (3 x)))

What is the integral of x^2+6e^x+C ?
The integral of x^2+6e^x+C is (x^3)/3+6e^x+Cx+C