Question

how to integrate this problem...

Answer 1

\[170/(x^2\sqrt{144x^2-361)}\]

Answer 2

have you tried a trig sub ?

Answer 3

That's what I did, and I got a different answer from what I got on wolframalpha

Answer 4

\[\int\limits_{}^{}\frac{170 dx}{x^2 \sqrt{(12x)^2-361}}=\frac{170}{\sqrt{361}} \int\limits_{}^{} \frac{ dx}{x^2 \sqrt{(\frac{12 x}{\sqrt{361}})^2-1}}\\ \text{ then use } \sec(\theta)=\frac{12 x}{\sqrt{361}}\]

Answer 5

I got to this far....\[170(144)/19^3 \ln \left| \sin(x) \right| -\sin^2(x)/2\]

Answer 6

that seems wrong....

Answer 7

Oh, just cause that was an incomplete part of this question...

Answer 8

and the 19^3 is not multiplied to the ln|sin(x)|..... that stuff is in the numerator

Answer 9

I seen @zepdrix had some constant multiple times the integral of cos(x) w.r.t x.
that is what I have as well

Answer 10

Can I see your work to see where you went wrong

Answer 11

Yeah sure...gimme a sec.

Answer 12

seems like you missed what dx was in terms of theta

Answer 13

Didn't know that is supposed to change too...

Answer 14

\[x= \frac{19}{12} \sec(\theta) \\ dx=\frac{19}{12} \sec(\theta) \tan(\theta) d \theta \]

Answer 15

\[\int\limits\limits_{}^{}\frac{dx}{x^2 \sqrt{144x^2-361}} =\int\limits\limits_{}^{}\frac{\frac{19}{12} \sec(\theta) \tan(\theta) d \theta}{(\frac{19}{12})^2 \sec^2(\theta) \sqrt{(12\frac{19}{12} \sec(\theta))^2-361}} \]

Answer 16

\[\int\limits_{}^{}\frac{\frac{19}{12} \sec(\theta) \tan(\theta) d \theta}{\frac{19^2}{12^2} \sec^2(\theta) \sqrt{361 \sec^2(\theta)-361}} \\ \frac{19}{12} \cdot \frac{12^2}{19^2} \int\limits_{}^{} \frac{\sec(\theta) \tan(\theta)}{\sec^2(\theta) \sqrt{19^2} \sqrt{\sec^2(\theta)-1}} d \theta \\ \frac{19}{12} \frac{12^2}{19^2} \frac{1}{\sqrt{19^2}} \int\limits_{}^{} \frac{\sec(\theta) \tan(\theta)}{\sec^2(\theta) \sqrt{\tan^2(\theta)}} d \theta \]

Answer 17

so what happened to the 170 on the top??

Answer 18

we can attach it latter

Answer 19

ok.

Answer 20

but you should be able to simplify this and integrate the result

Answer 21

then multiply the 170

Answer 22

lemme try it...

Answer 23

and actually you will get exactly what wolfram got (or should )