What is the integral of-2cos(x)+3x^2-5x+4 ?

The integral of-2cos(x)+3x^2-5x+4 is -2sin(x)+x^3-(5x^2)/2+4x+C

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integral of-2cos(x)+3x^2-5x+4

\int - 2 cos (x) + 3 x^{2} - 5 x + 4 d x

- 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

Solution steps

\int - 2 cos (x) + 3 x^{2} - 5 x + 4 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 2 cos (x) d x + \int 3 x^{2} d x - \int 5 x d x + \int 4 d x

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

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= - 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x

Add a constant to the solution

= - 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

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What is the integral of-2cos(x)+3x^2-5x+4 ?
The integral of-2cos(x)+3x^2-5x+4 is -2sin(x)+x^3-(5x^2)/2+4x+C