## anonymous 5 years ago compute the indefinite integral: dx/(x^2+4)^(5/2)

1. anonymous

If I'm not mistaken, you can use trigonometric substitution : you have the following: $\int\limits_{}^{}1/\sqrt{(x^2 + 4)^5}dx$ we have the form : $\sqrt{x^2 + a^2}$ so you can let x be: $x = a \tan \theta$ Then substitute x in : $\sqrt{(x^2 + 4)^5}$ After that find dx when x = atan(theta) Last , susbstitute everything in the integral and then integrate. Give it a try now ^_^

2. anonymous

thank you so much!

3. anonymous

i also have another question...the original question is: compute the integral: ∫01(8x2+6)/(x2+1)(x+7)dx

4. anonymous

∫(8x2+6)/(x2+1)(x+7)dx

5. anonymous

np :)

6. anonymous

use partial fractions for this one so you'll have the following form:$= (A/x^2 + 1) + (B/x+7)$ try it out ^_^

7. anonymous

and after that you plug in the value right?

8. anonymous

you'll have to multiply by the denominators to get the following state: $8x^2 +6 = A(x+7) + B(x^2+1)$ then try out small numbers for x, then plug it in ^_^

9. anonymous

example, take x = 0 then x = 1 :)

10. anonymous

to get values for A and B, then find the integral :)

11. anonymous

thanks you are a BIG HELP!

12. anonymous

you're welcome, glad I could help ^_^

13. anonymous

$\int\limits_{0}^{1} \ln(x) / x ^{1/2} dx$ to approximate this integral using the trapezoid rule. if you can help me with this one also, i am sorry :(