What is the integral of (3x^2+2e^x) ?

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

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integral of (3x^2+2e^x)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

x \to 0 + lim (\frac{∣ x sin ( x ) ∣}{x})

\frac{d}{d x} (sin (e^{5 x}))

\int_{1}^{e} ln (15 x) d x

\frac{d}{d x} (- \frac{20}{( 2 + x ) ^{2}})

e^{x} - \frac{8}{x}