What is the integral of (x^2+2sin(x)-1/x) ?

The integral of (x^2+2sin(x)-1/x) is (x^3)/3-2cos(x)-ln|x|+C

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integral of (x^2+2sin(x)-1/x)

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

\frac{x ^{3}}{3} - 2 cos (x) - ln ∣ x ∣ + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{3}}{3} - 2 cos (x) - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 cos (x) - ln ∣ x ∣ + C

What is the integral of (x^2+2sin(x)-1/x) ?
The integral of (x^2+2sin(x)-1/x) is (x^3)/3-2cos(x)-ln|x|+C