What is the integral of (5x^{1/4}-5x^{-6}+1) ?

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

Popular >

integral of (5x^{1/4}-5x^{-6}+1)

\int (5 x^{\frac{1}{4}} - 5 x^{- 6} + 1) d x

4 x^{\frac{5}{4}} + \frac{1}{x ^{5}} + x + C

Solution steps

\int 5 x^{\frac{1}{4}} - 5 x^{- 6} + 1 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 5 x^{- 6} d x + \int 1 d x

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

\int 5 x^{- 6} d x = - \frac{1}{x ^{5}}

\int 1 d x = x

= 4 x^{\frac{5}{4}} - (- \frac{1}{x ^{5}}) + x

Simplify

= 4 x^{\frac{5}{4}} + \frac{1}{x ^{5}} + x

Add a constant to the solution

= 4 x^{\frac{5}{4}} + \frac{1}{x ^{5}} + x + C

\int \frac{x ^{3} + 2 x ^{2} + 5 x + 12}{x + 2} d x

\int 5 tan (t) d t

\int \frac{7 ^{c o t (2 x)}}{sin ^{2} ( 2 x )} d x

\int + \frac{2 x ^{2} - 9 x - 9}{x ^{3} - 9 x} d x

\int e^{3 x} (x^{2} + y^{2}) d y

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