Evaluate the following intcsc^6udu

Khadija Wells

Khadija Wells

Answered question

2021-03-09

Evaluate the following
csc6udu

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2021-03-10Added 97 answers

The trigonometric function csc6udu
csc6udu=csc4ucsc2udu
=(csc2u)2csc2udu
=(1+cot2u)2csc2udu
(Since, csc2u=1+cot2u)
Let t=cotu
dtdu=csc2u implies dt=csc2udu
Now, csc6du=(1+t2)dt
=(1+2t2+t4)dt
=(t+2t33+t55)+C
=t2t33t55+C
Here t=cotu
Therefore, csc6udu=cotu23cot3u15cot5u+C

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