What is the integral of 3^x+x^3+3/x ?

The integral of 3^x+x^3+3/x is (3^x}{ln(3)}+\frac{x^4)/4+3ln|x|+C

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integral of 3^x+x^3+3/x

\int 3^{x} + x^{3} + \frac{3}{x} d x

\frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

Solution steps

\int 3^{x} + x^{3} + \frac{3}{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} d x + \int x^{3} d x + \int \frac{3}{x} d x

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

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What is the integral of 3^x+x^3+3/x ?
The integral of 3^x+x^3+3/x is (3^x}{ln(3)}+\frac{x^4)/4+3ln|x|+C