What is the integral of 3x^3-1/x+5e^x ?

The integral of 3x^3-1/x+5e^x is (3x^4)/4-ln|x|+5e^x+C

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integral of 3x^3-1/x+5e^x

\int 3 x^{3} - \frac{1}{x} + 5 e^{x} d x

\frac{3 x ^{4}}{4} - ln ∣ x ∣ + 5 e^{x} + C

Solution steps

\int 3 x^{3} - \frac{1}{x} + 5 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^{3} d x - \int \frac{1}{x} d x + \int 5 e^{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 5 e^{x} d x = 5 e^{x}

= \frac{3 x ^{4}}{4} - ln ∣ x ∣ + 5 e^{x}

Add a constant to the solution

= \frac{3 x ^{4}}{4} - ln ∣ x ∣ + 5 e^{x} + C

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What is the integral of 3x^3-1/x+5e^x ?
The integral of 3x^3-1/x+5e^x is (3x^4)/4-ln|x|+5e^x+C