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

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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

f (x) = \frac{4 x ^{\frac{3}{2}}}{x}

\frac{x ^{2} + 8 x + 3}{x}

\frac{3}{5}

\frac{d}{d x} (cos (5 x - 9))

\frac{2 s}{s ^{2} + s}

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