Question

Maths . Integrate Tan x ​

Answer 1

${ \sf{Hey!}} \\ \\ \implies \: \int \: tan \: x \: dx \\ \\ \implies \: \int \: \dfrac{sin \: x}{cos \: x \: } \: dx \:$

Now we can use the method of substitution here.

→ Put Cos x = t

=> -(Sin x) dx = dt [ differentiating w.r.t x ]

•°• Sin x dx = -dt -----------------eqn. (1)

Put this value into the integral.

$\implies - \: \int \dfrac{1}{t} \: \: dt \\ \\ \\ \implies \: \: - log |t| + c$

Put the value of t again we get the solved integral as

$\: \implies \: \int \: tan \: x \: dx \: = - log |cos \: x| + c \: \\ \\ or \: = > log |sec \: x \: | + c$

[ As Cos x = 1/Sec x]

Answer 2

Answer:

Integral tan(x) tan x = - ln|cos x| + C.