What is the integral of x^{1/4}+6 ?

The integral of x^{1/4}+6 is 4/5 x^{5/4}+6x+C

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integral of x^{1/4}+6

\int x^{\frac{1}{4}} + 6 d x

\frac{4}{5} x^{\frac{5}{4}} + 6 x + C

Solution steps

\int x^{\frac{1}{4}} + 6 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^{\frac{1}{4}} d x + \int 6 d x

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

\int 6 d x = 6 x

= \frac{4}{5} x^{\frac{5}{4}} + 6 x

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{4}} + 6 x + C

\int \frac{sin ( 2 x )}{1 + 3 cos ^{2} ( x )} d x

\int 4 sin (6 x) d x

\int \frac{x ^{2} + 2 x + 3}{x + 1} d x

What is the integral of x^{1/4}+6 ?
The integral of x^{1/4}+6 is 4/5 x^{5/4}+6x+C