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

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

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

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

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Simplify

sin (x) (tan (x) + cot (x)) : sec (x)

= \int sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

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