What is the integral of (12x^{3/4}-9x^{5/3}) ?

The integral of (12x^{3/4}-9x^{5/3}) is 48/7 x^{7/4}-27/8 x^{8/3}+C

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integral of (12x^{3/4}-9x^{5/3})

\int (12 x^{\frac{3}{4}} - 9 x^{\frac{5}{3}}) d x

\frac{48}{7} x^{\frac{7}{4}} - \frac{27}{8} x^{\frac{8}{3}} + C

Solution steps

\int 12 x^{\frac{3}{4}} - 9 x^{\frac{5}{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 12 x^{\frac{3}{4}} d x - \int 9 x^{\frac{5}{3}} d x

\int 12 x^{\frac{3}{4}} d x = \frac{48}{7} x^{\frac{7}{4}}

\int 9 x^{\frac{5}{3}} d x = \frac{27}{8} x^{\frac{8}{3}}

= \frac{48}{7} x^{\frac{7}{4}} - \frac{27}{8} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{48}{7} x^{\frac{7}{4}} - \frac{27}{8} x^{\frac{8}{3}} + C

What is the integral of (12x^{3/4}-9x^{5/3}) ?
The integral of (12x^{3/4}-9x^{5/3}) is 48/7 x^{7/4}-27/8 x^{8/3}+C