What is the integral of (5x^2+2/(x^4)-3\sqrt[3]{x}) ?

The integral of (5x^2+2/(x^4)-3\sqrt[3]{x}) is (5x^3)/3-2/(3x^3)-9/4 x^{4/3}+C

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integral of (5x^2+2/(x^4)-3\sqrt[3]{x})

\frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}} + 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 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

= \frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{5 x ^{3}}{3} - \frac{2}{3 x ^{3}} - \frac{9}{4} x^{\frac{4}{3}} + C

x \to 5 lim (\frac{4 x}{x - 5})

y^{^{'}} = (t + y)^{2} - 1, y (3) = 6

\int \frac{( x ^{2} + 3 x - 4 )}{x ^{3} - 4 x ^{2} + 4 x} d x

y = 4 x^{2}, x = 1, y = 0

\frac{2 e ^{- 2 s}}{5 s ^{2} + 45}

What is the integral of (5x^2+2/(x^4)-3\sqrt[3]{x}) ?
The integral of (5x^2+2/(x^4)-3\sqrt[3]{x}) is (5x^3)/3-2/(3x^3)-9/4 x^{4/3}+C