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

The integral of (x^3-3e^x) is (x^4)/4-3e^x+C

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integral of (x^3-3e^x)

\int (x^{3} - 3 e^{x}) d x

\frac{x ^{4}}{4} - 3 e^{x} + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} - 3 e^{x}

Add a constant to the solution

= \frac{x ^{4}}{4} - 3 e^{x} + C

\int (12 - x)^{2} d x

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\int \frac{e ^{4 x}}{9 - 4 e ^{4 x}} d x

\int x^{2} (2 x^{3} + 3)^{5} d x

What is the integral of (x^3-3e^x) ?
The integral of (x^3-3e^x) is (x^4)/4-3e^x+C