What is the integral of (tan(x))/(sin(x)) ?

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

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integral of (tan(x))/(sin(x))

\int \frac{tan ( x )}{sin ( x )} d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{tan ( x )}{sin ( x )} d x

Simplify

\frac{tan ( x )}{sin ( 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 (tan(x))/(sin(x)) ?
The integral of (tan(x))/(sin(x)) is ln|tan(x)+sec(x)|+C