What is the integral of 4x^2-sin(x)+2 ?

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

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integral of 4x^2-sin(x)+2

\int 4 x^{2} - sin (x) + 2 d x

\frac{4 x ^{3}}{3} + cos (x) + 2 x + C

Solution steps

\int 4 x^{2} - sin (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 4 x^{2} d x - \int sin (x) d x + \int 2 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

\int 2 d x = 2 x

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

Simplify

= \frac{4 x ^{3}}{3} + cos (x) + 2 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + cos (x) + 2 x + C

(1 - \frac{4}{x + 2})^{3}

5 tan (x), at x = \frac{π}{3}

\frac{d}{d x} (arctan (\frac{x}{y}))

\frac{x ^{2}}{e ^{x}}

\int_{0}^{1} e^{- 4 x} d x

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