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

The integral of (tan(x))/(csc(x)+cot(x)) is -x+ln|tan(x)+sec(x)|+C

Popular >

integral of (tan(x))/(csc(x)+cot(x))

\int \frac{tan ( x )}{csc ( x ) + cot ( x )} d x

- x + ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{tan ( x )}{csc ( x ) + cot ( x )} d x

Rewrite using trig identities

= \int \frac{sin ^{2} ( x )}{cos ( x ) ( 1 + cos ( x ) )} d x

Rewrite using trig identities

= \int - 1 + sec (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 1 d x + \int sec (x) d x

\int 1 d x = x

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

= - x + ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - x + ln ∣ tan (x) + sec (x) ∣ + C

\frac{d}{d x} (4 x^{5} + 2 x^{3} + 6 x^{2} + 3 x)

\int 8 e^{2 θ} sin (2 θ) d θ

y^{^{'}} + y = x \cdot e^{- x} + 1

2 x^{3} + 36 x^{2} + 210 x + 11

\int a x^{3} d x

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