Question

integral of 54/(x^2+8x+97) dx, x=9tan t-4

Answer 1

complete the square of the denominator and make a trig substitution

Answer 2

do you know how to complete the square?

Answer 3

no i not.

Answer 4

How??? a student study integral but do not know how to complete the square??????

Answer 5

I knew how to at one point, but it has been awhile.

Answer 6

ok, we have:
x^2+8x+97, but (x+4)^2 = x^2 + 8x + 16, so we need to add more 81 units to get the same thing, so:
x^2+8x+97 = (x+4)^2 + 81

Answer 7

okay makes sense.

Answer 8

now make a trig substitution, like x+4 = tan^2(u)

Answer 9

sorry, not this

Answer 10

call (x+4)/9 = tan^2(u)

Answer 11

okay

Answer 12

support: let (x+4) = 9tan u

Answer 13

yes that's right

Answer 14

square both sides: (x+4)^2 =81 tan^2 u

Answer 15

sorry hahaha

Answer 16

@M4thM1nd continue your stuff, please

Answer 17

now on is pretty straightforward

Answer 18

do you know how to continue @lanarose21 ?

Answer 19

u sub?

Answer 20

after you complete the square, call (x+4)/9 = tan(u)

Answer 21

okay. I did that!

Answer 22

remenber that tan^2(u) + 1 = sec^2(u)

Answer 23

okay

Answer 24

so where are you stuck?

Answer 25

getting the final answer. like simplifying all of it.

Answer 26

Refer to the Mathematica attachment.

Answer 27

Thank you!