What is the integral of (x^2-15/2 sqrt(x)+x^{-4/3}) ?

The integral of (x^2-15/2 sqrt(x)+x^{-4/3}) is (x^3)/3-5x^{3/2}-3/(\sqrt[3]{x)}+C

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integral of (x^2-15/2 sqrt(x)+x^{-4/3})

\int (x^{2} - \frac{15}{2} x + x^{- \frac{4}{3}}) d x

Solution steps

\int x^{2} - \frac{15}{2} x + x^{- \frac{4}{3}} 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 x^{2} d x - \int \frac{15}{2} x d x + \int x^{- \frac{4}{3}} d x

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

\int \frac{15}{2} x d x = 5 x^{\frac{3}{2}}

\int x^{- \frac{4}{3}} d x = - \frac{3}{x ^{\frac{1}{3}}}

= \frac{x ^{3}}{3} - 5 x^{\frac{3}{2}} - \frac{3}{x ^{\frac{1}{3}}}

Apply radical rule:

Add a constant to the solution

\int \frac{x}{2 - 3 x} d x

\frac{d y}{d x} = (x - 10)^{2}

e^{x} + 1

f (x) = x^{2} - 1, (5, 24)

\int_{0}^{\frac{π}{2}} (cos^{2} (x)) d x

What is the integral of (x^2-15/2 sqrt(x)+x^{-4/3}) ?
The integral of (x^2-15/2 sqrt(x)+x^{-4/3}) is (x^3)/3-5x^{3/2}-3/(\sqrt[3]{x)}+C