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

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

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

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

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

Solution steps

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

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

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

= - 4 cos (x) + \frac{2 x ^{5}}{5} - 2 x

Add a constant to the solution

= - 4 cos (x) + \frac{2 x ^{5}}{5} - 2 x + C

x \to 0 lim (x (x - [x]))

ma c l a u r in (1 + x)^{\frac{1}{6}}

\int_{0}^{2 π} ∣ sin (x) ∣ d x

\frac{d}{d x} (\frac{x}{9 + x ^{2}})

\int_{1}^{e^{5}} x^{3} ln (x) d x

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