What is the integral of (3\sqrt[3]{x^4}-3x+2/x) ?

The integral of (3\sqrt[3]{x^4}-3x+2/x) is 9/7 x^{7/3}-(3x^2)/2+2ln|x|+C

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integral of (3\sqrt[3]{x^4}-3x+2/x)

\frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ 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 3 x d x = \frac{3 x ^{2}}{2}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{9}{7} x^{\frac{7}{3}} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣ + C

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What is the integral of (3\sqrt[3]{x^4}-3x+2/x) ?
The integral of (3\sqrt[3]{x^4}-3x+2/x) is 9/7 x^{7/3}-(3x^2)/2+2ln|x|+C