What is the integral of 2x^3-8/(3x^3)+\sqrt[4]{x^3} ?

The integral of 2x^3-8/(3x^3)+\sqrt[4]{x^3} is (x^4)/2+4/(3x^2)+4/7 x^{7/4}+C

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integral of 2x^3-8/(3x^3)+\sqrt[4]{x^3}

\frac{x ^{4}}{2} + \frac{4}{3 x ^{2}} + \frac{4}{7} x^{\frac{7}{4}} + 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 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{8}{3 x ^{3}} d x = - \frac{4}{3 x ^{2}}

= \frac{x ^{4}}{2} - (- \frac{4}{3 x ^{2}}) + \frac{4}{7} x^{\frac{7}{4}}

Simplify

= \frac{x ^{4}}{2} + \frac{4}{3 x ^{2}} + \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{4}{3 x ^{2}} + \frac{4}{7} x^{\frac{7}{4}} + C

y = 2 x^{3}, (- 1, - 2)

\int tan (y) d y

\int \frac{x ^{6} e ^{x} - 4 x ^{5}}{x ^{6}} d x

x \to π - lim ((x - π) csc (x))

f (x) = \frac{4 x - 7}{28 x ^{5}}

What is the integral of 2x^3-8/(3x^3)+\sqrt[4]{x^3} ?
The integral of 2x^3-8/(3x^3)+\sqrt[4]{x^3} is (x^4)/2+4/(3x^2)+4/7 x^{7/4}+C