this-trig-integral-has-quite-a-few-insights-on-trig-integrals-andd-u-subs-as-well-as-on-the-properties-of-logarithms-try-it-out-it-s-a-nice-one-tan-x-dx-

Question Number 91074 by M±th+et+s last updated on 27/Apr/20

t h i s t r i g i n t e g r a l h a s q u i t e a f e w

i n s i g h t s o n t r i g i n t e g r a l s a n d d

u s u b s a s w e l l a s o n t h e p r o p e r t i e s

o f l o g a r i t h m s . t r y i t o u t {i t}^{'} s a n i c e

o n e

\int t a n (x) d x

Commented by mathmax by abdo last updated on 28/Apr/20

\int t a n x d x = \int \frac{s i n x}{c o s x} d x = - \int \frac{d (c o s x)}{c o s x} = - l n ∣ c o s x ∣ + C

Answered by MWSuSon last updated on 27/Apr/20

{i s n}^{'} t t h i s j u s t - {l o g}_{e} \cos (x) + C o r a m i

m i s s i n g s o m e t h i n g ?

Commented by M±th+et+s last updated on 28/Apr/20

t h e r e i s a n o t h e r s o l u t i o n s l i k e

\frac{1}{2} l n (1 + {t a n}^{2} (x)) + c

Commented by abdomathmax last updated on 28/Apr/20

y e s b e c a u s e 1 + {t a n}^{2} x = \frac{1}{{c o s}^{2} x} \to t h e s a m e r e s u l t