Question

evaluate the integral: \[\int\limits_{}^{} \tan x \space dx\]

Answer 1

write tan x = sin x/ cos x first.

Answer 2

by parts?

Answer 3

no...by substitution.

Answer 4

\[\int\limits_{}^{} \frac{\sin x}{\cos x} \space dx\]

Answer 5

yes, now what can you substitute to get the form,\(\int f'(x)/f(x) dx = \log |f(x)|+c\)

Answer 6

sorry, i can't get u :/

Answer 7

this is a standard result which you'll use here
\(\large \int \dfrac{f'(x)}{f(x) }dx = \log |f(x)|+c\)
so, when you see the derivative of denominator in numerator, you can directly use this.
here, can you see derivative of denominator in numerator ?

Answer 8

whats derivative of cos x ?

Answer 9

sin x

Answer 10

sure?

Answer 11

- sin x

Answer 12

yes.
\(-\int\limits_{}^{} \frac{-\sin x}{\cos x} \space dx\)
now can you use that standard result to integrate this ?

Answer 13

yeah i gt it;
thank u very much :)

Answer 14

welcome ^_^

Answer 15

what's the problem when we substitute sinx?

Answer 16

then dx=.. ?

Answer 17

got it