What is the integral of 3x^2-2x+7e^x ?

The integral of 3x^2-2x+7e^x is x^3-x^2+7e^x+C

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integral of 3x^2-2x+7e^x

\int 3 x^{2} - 2 x + 7 e^{x} d x

x^{3} - x^{2} + 7 e^{x} + C

Solution steps

\int 3 x^{2} - 2 x + 7 e^{x} 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 x^{2} d x - \int 2 x d x + \int 7 e^{x} d x

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

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

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

= x^{3} - x^{2} + 7 e^{x}

Add a constant to the solution

= x^{3} - x^{2} + 7 e^{x} + C

\int (x + 2) (x - 5)^{4} d x

\int \frac{2}{( x + 1 ) ( x - 4 )} d x

\int 7 x^{2} (- 2 x^{3} - 5)^{6} d x

\int \frac{x ^{3}}{x ^{2} + 8 x + 16} d x

What is the integral of 3x^2-2x+7e^x ?
The integral of 3x^2-2x+7e^x is x^3-x^2+7e^x+C