What is the integral of 5x^{4/3}+4x^{5/4} ?

The integral of 5x^{4/3}+4x^{5/4} is 15/7 x^{7/3}+16/9 x^{9/4}+C

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integral of 5x^{4/3}+4x^{5/4}

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

\frac{15}{7} x^{\frac{7}{3}} + \frac{16}{9} x^{\frac{9}{4}} + C

Solution steps

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

\int 5 x^{\frac{4}{3}} d x = \frac{15}{7} x^{\frac{7}{3}}

\int 4 x^{\frac{5}{4}} d x = \frac{16}{9} x^{\frac{9}{4}}

= \frac{15}{7} x^{\frac{7}{3}} + \frac{16}{9} x^{\frac{9}{4}}

Add a constant to the solution

= \frac{15}{7} x^{\frac{7}{3}} + \frac{16}{9} x^{\frac{9}{4}} + C

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What is the integral of 5x^{4/3}+4x^{5/4} ?
The integral of 5x^{4/3}+4x^{5/4} is 15/7 x^{7/3}+16/9 x^{9/4}+C