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

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

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

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

e^{x} + \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

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

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

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

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

= e^{x} + \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= e^{x} + \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3} + C

\frac{1}{3 x ^{5}}

\int_{1}^{2} (6 x - 1) d x

f (x) = \frac{2 x}{x + 1}, (1, 1)

\int sin^{5} (4 x) cos^{3} (4 x) d x

f (x) = x^{4} + 2 x

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