What is the integral of (x^{-1}+x^2+2cos(x)+4sin(x)) ?

The integral of (x^{-1}+x^2+2cos(x)+4sin(x)) is ln|x|+(x^3)/3+2sin(x)-4cos(x)+C

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integral of (x^{-1}+x^2+2cos(x)+4sin(x))

\int (x^{- 1} + x^{2} + 2 cos (x) + 4 sin (x)) d x

ln ∣ x ∣ + \frac{x ^{3}}{3} + 2 sin (x) - 4 cos (x) + C

Solution steps

\int x^{- 1} + x^{2} + 2 cos (x) + 4 sin (x) 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^{- 1} d x + \int x^{2} d x + \int 2 cos (x) d x + \int 4 sin (x) d x

\int x^{- 1} d x = ln ∣ x ∣

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

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

\int 4 sin (x) d x = - 4 cos (x)

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

Add a constant to the solution

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

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\int tan (x) tan (x) d x

What is the integral of (x^{-1}+x^2+2cos(x)+4sin(x)) ?
The integral of (x^{-1}+x^2+2cos(x)+4sin(x)) is ln|x|+(x^3)/3+2sin(x)-4cos(x)+C