What is the integral of (\sqrt[3]{x}-(10)/(x-5)+e^x) ?

The integral of (\sqrt[3]{x}-(10)/(x-5)+e^x) is 3/4 x^{4/3}-10ln|x-5|+e^x+C

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integral of (\sqrt[3]{x}-(10)/(x-5)+e^x)

\frac{3}{4} x^{\frac{4}{3}} - 10 ln ∣ x - 5 ∣ + e^{x} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int \frac{10}{x - 5} d x = 10 ln ∣ x - 5 ∣

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

= \frac{3}{4} x^{\frac{4}{3}} - 10 ln ∣ x - 5 ∣ + e^{x}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} - 10 ln ∣ x - 5 ∣ + e^{x} + C

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What is the integral of (\sqrt[3]{x}-(10)/(x-5)+e^x) ?
The integral of (\sqrt[3]{x}-(10)/(x-5)+e^x) is 3/4 x^{4/3}-10ln|x-5|+e^x+C