What is the integral of (tan(x)+x^{-1}-2x+3) ?

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

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integral of (tan(x)+x^{-1}-2x+3)

\int (tan (x) + x^{- 1} - 2 x + 3) d x

- ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x + C

Solution steps

\int tan (x) + x^{- 1} - 2 x + 3 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 tan (x) d x + \int x^{- 1} d x - \int 2 x d x + \int 3 d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int x^{- 1} d x = ln ∣ x ∣

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

\int 3 d x = 3 x

= - ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x

Add a constant to the solution

= - ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x + C

\int \frac{1}{100 + 2 x} d x

\int e^{\frac{x}{2}} cos (2 x) d x

\int (8 x - 4 x^{- 1}) d x

ln (2 x)

\int (x + x^{2}) d x

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