How do I integrate x 2 </msup> <msqrt> 9

gnatopoditw

gnatopoditw

Answered question

2022-06-14

How do I integrate x 2 9 x 2 + 15 ?

Answer & Explanation

crociandomh

crociandomh

Beginner2022-06-15Added 19 answers

Lets start with
3 x 15 = tan u
so that
9 x 2 + 15 15 = sec u .
With
d x = 15 3 sec 2 u d u
we get
x 2 9 x 2 + 15 d x = 15 9 tan 2 u 15 sec u 15 3 sec 2 u d u = 15 27 tan 2 u sec u d u = 5 9 ( sec 2 u 1 ) sec u d u = 5 9 ( sec 3 u sec u ) d u = 5 9 [ sec u tan u 2 + ln | sec u + tan u | 2 ln | sec u + tan u | ] + C = 5 18 [ sec u tan u ln | sec u + tan u | ] + C = 5 18 [ ( 9 x 2 + 15 ) 3 x 15 ln | 9 x 2 + 15 + 3 x 15 | ] + C

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