What is the integral of x^2+7e^x+C ?

The integral of x^2+7e^x+C is (x^3)/3+7e^x+Cx+C

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integral of x^2+7e^x+C

\int x^{2} + 7 e^{x} + C d x

\frac{x ^{3}}{3} + 7 e^{x} + C x + C

Solution steps

\int x^{2} + 7 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 7 e^{x} d x + \int C d x

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

\int 7 e^{x} d x = 7 e^{x}

\int C d x = C x

= \frac{x ^{3}}{3} + 7 e^{x} + C x

Add a constant to the solution

= \frac{x ^{3}}{3} + 7 e^{x} + C x + C

y^{^{''}} + 2 y^{^{'}} = 1

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{( - 3 e ^{5 x} )}{( x ^{2} + 1 )}

\frac{d}{d x} (- 2 + \frac{7}{4 x})

12 x

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

What is the integral of x^2+7e^x+C ?
The integral of x^2+7e^x+C is (x^3)/3+7e^x+Cx+C