What is the integral of 1/(sin(x)cos(x)) ?

The integral of 1/(sin(x)cos(x)) is ln|tan(x)|+C

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integral of 1/(sin(x)cos(x))

\int \frac{1}{sin ( x ) cos ( x )} d x

ln ∣ tan (x) ∣ + C

Solution steps

\int \frac{1}{sin ( x ) cos ( x )} d x

Rewrite using trig identities

= \int \frac{sec ( x )}{sin ( x )} d x

Apply Trigonometric Substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = tan (x)

= ln ∣ tan (x) ∣

Add a constant to the solution

= ln ∣ tan (x) ∣ + C

x \to - 2 lim (\frac{z + 2}{x ^{2} + 4})

\int 3 sec^{2} (x) tan (x) d x

x \to 3 lim (I n (x^{2} - 9))

\int e^{a x} sin (b) x d x

\frac{\partial}{\partial y} (y arcsin (x y))

What is the integral of 1/(sin(x)cos(x)) ?
The integral of 1/(sin(x)cos(x)) is ln|tan(x)|+C