Integral Calculus Question 481
Question: $ \int{cose{c^{4}}x,dx}= $
[RPET 2002]
Options:
A) $ \cot x+\frac{{{\cot }^{3}}x}{3}+c $
B) $ \tan x+\frac{{{\tan }^{3}}x}{3}+c $
C) $ -\cot x-\frac{{{\cot }^{3}}x}{3}+c $
D) $ -\tan x-\frac{{{\tan }^{3}}x}{3}+c $
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Answer:
Correct Answer: C
Solution:
$ =-\log ({{\cos }^{-1}}x)+c. $ $ =\int{cose{c^{2}}x}.,cose{c^{2}}xdx $ $ =\int{cose{c^{2}}x(1+{{\cot }^{2}}x),dx} $ $ =\int{cose{c^{2}}xdx}+\int{{{\cot }^{2}}x.,cose{c^{2}}x,dx} $ $ =-\cot x-\frac{{{\cot }^{3}}x}{3}+c $ .
BETA
