What is the integral of 6x^{2/3}-8x^{3/4} ?

The integral of 6x^{2/3}-8x^{3/4} is 18/5 x^{5/3}-32/7 x^{7/4}+C

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integral of 6x^{2/3}-8x^{3/4}

\int 6 x^{\frac{2}{3}} - 8 x^{\frac{3}{4}} d x

\frac{18}{5} x^{\frac{5}{3}} - \frac{32}{7} x^{\frac{7}{4}} + C

Solution steps

\int 6 x^{\frac{2}{3}} - 8 x^{\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 6 x^{\frac{2}{3}} d x - \int 8 x^{\frac{3}{4}} d x

\int 6 x^{\frac{2}{3}} d x = \frac{18}{5} x^{\frac{5}{3}}

\int 8 x^{\frac{3}{4}} d x = \frac{32}{7} x^{\frac{7}{4}}

= \frac{18}{5} x^{\frac{5}{3}} - \frac{32}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{18}{5} x^{\frac{5}{3}} - \frac{32}{7} x^{\frac{7}{4}} + C

x \to 1 + lim (ln (x))

\frac{d ^{2}}{d x ^{2}} (e^{5 e^{x}})

\int e^{7 x + 5} d x

\frac{d}{d x} (4 (5 - 9 x)^{5})

\frac{d}{d x} (tan^{l n (5 x)} (cos (x)))

What is the integral of 6x^{2/3}-8x^{3/4} ?
The integral of 6x^{2/3}-8x^{3/4} is 18/5 x^{5/3}-32/7 x^{7/4}+C