What is the integral of cos(x)+6sin(x)+3x^2 ?

The integral of cos(x)+6sin(x)+3x^2 is sin(x)-6cos(x)+x^3+C

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integral of cos(x)+6sin(x)+3x^2

\int cos (x) + 6 sin (x) + 3 x^{2} d x

sin (x) - 6 cos (x) + x^{3} + C

Solution steps

\int cos (x) + 6 sin (x) + 3 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 cos (x) d x + \int 6 sin (x) d x + \int 3 x^{2} d x

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

\int 6 sin (x) d x = - 6 cos (x)

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

= sin (x) - 6 cos (x) + x^{3}

Add a constant to the solution

= sin (x) - 6 cos (x) + x^{3} + C

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What is the integral of cos(x)+6sin(x)+3x^2 ?
The integral of cos(x)+6sin(x)+3x^2 is sin(x)-6cos(x)+x^3+C