Question

integral problem substitution

Answer 1

\[\int\limits_{?}^{?}\frac{ 40 }{ x ^{2}+25 }\]

Answer 2

it's an indefinite integral

Answer 3

\[put~ x=5 \tan t,dx=5 \sec ^2 t~dt\]
complete it.

Answer 4

we havent learned trig substitution yet

Answer 5

i dont know how

Answer 6

What have you learned then?

Answer 7

u substitution and integration by parts

Answer 8

What about letting \(u=(x^2+25)^{-1}\quad dv =40\;dx\)?

Answer 9

Am I able to integrate by parts and then u substitute because now I am getting \[\frac{ 40x }{ x ^{2}+25 }-\int\limits_{?}^{?}\frac{ -40x }{ (x ^{2}+25)^{2} }\]

Answer 10

was was your du and v?

Answer 11

du was -(x^2+25)^-2 and v was 40x

Answer 12

if you use chain rule, where is the derivative of the inner function.

Answer 13

left that out sorry

Answer 14

was I close though?

Answer 15

Im still lost ecause the 2x just means that I now have the same problem but the integral is -80x^2 over (x^2+25)^-2

Answer 16

Dunno, this is supposed to be a trig substitution.

Answer 17

ill ask my teacher about it tomorrow thanks for your help though I appreciate it

Answer 18

You could let \(u=x/5\) and then let \(w = \tan^{-1}(u)\)