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

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

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integral of-sqrt(4x)-5/(3x^{4/3)}+3/4

\int - 4 x - \frac{5}{3 x ^{\frac{4}{3}}} + \frac{3}{4} d x

Solution steps

\int - 4 x - \frac{5}{3 x ^{\frac{4}{3}}} + \frac{3}{4} 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 4 x d x - \int \frac{5}{3 x ^{\frac{4}{3}}} d x + \int \frac{3}{4} d x

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

\int \frac{5}{3 x ^{\frac{4}{3}}} d x = - \frac{5}{x ^{\frac{1}{3}}}

\int \frac{3}{4} d x = \frac{3}{4} x

= - \frac{4}{3} x^{\frac{3}{2}} - (- \frac{5}{x ^{\frac{1}{3}}}) + \frac{3}{4} x

Simplify

Add a constant to the solution

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