What is the integral of tan(x)+2cot(x) ?

The integral of tan(x)+2cot(x) is -ln|cos(x)|+2ln|sin(x)|+C

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integral of tan(x)+2cot(x)

\int tan (x) + 2 cot (x) d x

- ln ∣ cos (x) ∣ + 2 ln ∣ sin (x) ∣ + C

Solution steps

\int tan (x) + 2 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 2 cot (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 2 cot (x) d x = 2 ln ∣ sin (x) ∣

= - ln ∣ cos (x) ∣ + 2 ln ∣ sin (x) ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + 2 ln ∣ sin (x) ∣ + C

\int \frac{sec ( 7 x )}{7} d x

\int \frac{1}{100 x - x ^{2}} d x

\int (5 x^{3} - 7 x^{2} + 3 x + 4) d x

y = x^{2} + 5

- cos (3 x) 3

What is the integral of tan(x)+2cot(x) ?
The integral of tan(x)+2cot(x) is -ln|cos(x)|+2ln|sin(x)|+C