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

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

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

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

- \frac{1}{x} + ln ∣ x ∣ + x + \frac{x ^{2}}{2} + sin (x) + C

Solution steps

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

\int x^{- 2} d x = - \frac{1}{x}

\int x^{- 1} d x = ln ∣ x ∣

\int 1 d x = x

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

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

= - \frac{1}{x} + ln ∣ x ∣ + x + \frac{x ^{2}}{2} + sin (x)

Add a constant to the solution

= - \frac{1}{x} + ln ∣ x ∣ + x + \frac{x ^{2}}{2} + sin (x) + C

n = 1 \sum \infty \frac{1}{2 \cdot n}

\frac{x}{x + 5}

\int \frac{4}{64 - 36 x ^{2}} d x

\frac{d}{d x} (3 π)

x \to 2 - lim (9 - x^{2})

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