What is the integral of 4sin(2x)+(2x^5-sqrt(x))/x ?

The integral of 4sin(2x)+(2x^5-sqrt(x))/x is -2cos(2x)+(2x^5)/5-2sqrt(x)+C

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integral of 4sin(2x)+(2x^5-sqrt(x))/x

\int 4 sin (2 x) + \frac{2 x ^{5} - x}{x} d x

- 2 cos (2 x) + \frac{2 x ^{5}}{5} - 2 x + C

Solution steps

\int 4 sin (2 x) + \frac{2 x ^{5} - x}{x} 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 4 sin (2 x) d x + \int \frac{2 x ^{5} - x}{x} d x

\int 4 sin (2 x) d x = - 2 cos (2 x)

\int \frac{2 x ^{5} - x}{x} d x = \frac{2 x ^{5}}{5} - 2 x

= - 2 cos (2 x) + \frac{2 x ^{5}}{5} - 2 x

Add a constant to the solution

= - 2 cos (2 x) + \frac{2 x ^{5}}{5} - 2 x + C

What is the integral of 4sin(2x)+(2x^5-sqrt(x))/x ?
The integral of 4sin(2x)+(2x^5-sqrt(x))/x is -2cos(2x)+(2x^5)/5-2sqrt(x)+C