What is the integral of x^2+2cos(x)+3 ?

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

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integral of x^2+2cos(x)+3

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

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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