What is the integral of 3x^2+5cos(x)+2 ?

The integral of 3x^2+5cos(x)+2 is x^3+5sin(x)+2x+C

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integral of 3x^2+5cos(x)+2

\int 3 x^{2} + 5 cos (x) + 2 d x

x^{3} + 5 sin (x) + 2 x + C

Solution steps

\int 3 x^{2} + 5 cos (x) + 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 3 x^{2} d x + \int 5 cos (x) d x + \int 2 d x

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

\int 5 cos (x) d x = 5 sin (x)

\int 2 d x = 2 x

= x^{3} + 5 sin (x) + 2 x

Add a constant to the solution

= x^{3} + 5 sin (x) + 2 x + C

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What is the integral of 3x^2+5cos(x)+2 ?
The integral of 3x^2+5cos(x)+2 is x^3+5sin(x)+2x+C