What is the integral of e^{3ln(x)}+e^{3x} ?

The integral of e^{3ln(x)}+e^{3x} is (x^4)/4+1/3 e^{3x}+C

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integral of e^{3ln(x)}+e^{3x}

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

\frac{x ^{4}}{4} + \frac{1}{3} e^{3 x} + C

Solution steps

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

\int e^{3 l n (x)} d x = \frac{x ^{4}}{4}

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= \frac{x ^{4}}{4} + \frac{1}{3} e^{3 x}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{1}{3} e^{3 x} + C

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What is the integral of e^{3ln(x)}+e^{3x} ?
The integral of e^{3ln(x)}+e^{3x} is (x^4)/4+1/3 e^{3x}+C