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

The integral of (sqrt(x)+x^{3/4}) is 2/3 x^{3/2}+4/7 x^{7/4}+C

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

\int (x + x^{\frac{3}{4}}) d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{4}{7} x^{\frac{7}{4}} + C

Solution steps

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

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

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

= \frac{2}{3} x^{\frac{3}{2}} + \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{4}{7} x^{\frac{7}{4}} + C

\frac{d}{d x} (4 x - 4 x)

\int \frac{x}{1 + 25 x ^{4}} d x

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x \to \frac{π}{3} lim (sec (x))

x \to π lim (0.4)

What is the integral of (sqrt(x)+x^{3/4}) ?
The integral of (sqrt(x)+x^{3/4}) is 2/3 x^{3/2}+4/7 x^{7/4}+C