What is the integral of 5x^{1/4}-7x^{3/4} ?

The integral of 5x^{1/4}-7x^{3/4} is 4x^{5/4}-4x^{7/4}+C

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integral of 5x^{1/4}-7x^{3/4}

\int 5 x^{\frac{1}{4}} - 7 x^{\frac{3}{4}} d x

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

Solution steps

\int 5 x^{\frac{1}{4}} - 7 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 5 x^{\frac{1}{4}} d x - \int 7 x^{\frac{3}{4}} d x

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

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

= 4 x^{\frac{5}{4}} - 4 x^{\frac{7}{4}}

Add a constant to the solution

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

f (x) = \frac{7}{x}

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

\frac{- x ^{2} + x + 6}{e ^{x}}

ln (x^{2} - x + 1)

\int \frac{2 x ^{2}}{x ^{4} - 1} d x

What is the integral of 5x^{1/4}-7x^{3/4} ?
The integral of 5x^{1/4}-7x^{3/4} is 4x^{5/4}-4x^{7/4}+C