What is the integral of tan(x)+cot(x) ?

The integral of tan(x)+cot(x) is -ln|cos(x)|+ln|sin(x)|+C

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integral of tan(x)+cot(x)

\int tan (x) + cot (x) d x

- ln ∣ cos (x) ∣ + ln ∣ sin (x) ∣ + C

Solution steps

\int tan (x) + cot (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 tan (x) d x + \int cot (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int cot (x) d x = ln ∣ sin (x) ∣

= - ln ∣ cos (x) ∣ + ln ∣ sin (x) ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + ln ∣ sin (x) ∣ + C

f (x) = \frac{e ^{5 x}}{2 x - 5}

\int_{0}^{l n (3)} 2 e^{3 x} d x

\int (x^{3} + e x) x^{2} + e d x

- 4 x sin (2 x^{2})

f (x) = - 8 (4 x + 3)^{- 3}, at x = 3

What is the integral of tan(x)+cot(x) ?
The integral of tan(x)+cot(x) is -ln|cos(x)|+ln|sin(x)|+C