What is the integral of (cos(x)+2/x+x^2+2) ?

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

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integral of (cos(x)+2/x+x^2+2)

\int (cos (x) + \frac{2}{x} + x^{2} + 2) d x

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

Solution steps

\int cos (x) + \frac{2}{x} + x^{2} + 2 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 cos (x) d x + \int \frac{2}{x} d x + \int x^{2} d x + \int 2 d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

\int 2 d x = 2 x

= sin (x) + 2 ln ∣ x ∣ + \frac{x ^{3}}{3} + 2 x

Add a constant to the solution

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

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\int \frac{1}{2 cos ^{2} ( 3 x )} d x

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