2cot-2-2t-

Question Number 21701 by Isse last updated on 01/Oct/17

\int 2 {c o t}^{2} 2 t

Commented by Tikufly last updated on 01/Oct/17

I think your question should

be \int {2 \cot}^{2} 2 tdt

Answered by alex041103 last updated on 01/Oct/17

\int 2 {c o t}^{2} (2 t) d t

W e m a k e t h e s u b s t i t u t i o n

u = 2 t, d u = 2 d t

\int 2 {c o t}^{2} (2 t) d t = \int {c o t}^{2} (u) d u =

= \int \frac{{c o s}^{2} u}{{s i n}^{2} u} d u = \int c o s u \frac{c o s u}{{s i n}^{2} u} d u = I

N o w w e i n t e g r a t e b y p a r t s

x = c o s u d v = \frac{c o s u}{{s i n}^{2} u} d u

d x = - s i n u d u v = - \frac{1}{s i n u}

\Rightarrow I = - \frac{c o s u}{s i n u} - \int d u = - c o t (u) - u =

= - c o t (2 t) - 2 t + C

A n s . \int 2 {c o t}^{2} (2 t) d t = - c o t (2 t) - 2 t + C

Answered by Tikufly last updated on 01/Oct/17

If your question is

\int 2 {c o t}^{2} 2 t d t, t h e n

I = \int 2 ({c o s e c}^{2} 2 t - 1) d t

= \int 2 {c o s e c}^{2} 2 t - \int 2 d t

= - c o t 2 t - 2 t + C

Commented by Isse last updated on 01/Oct/17

t h n k s

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