Question

compute the indefinite integral: dx/(x^2+4)^(5/2)

Answer 1

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 ^_^

Answer 2

thank you so much!

Answer 3

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

Answer 4

∫(8x2+6)/(x2+1)(x+7)dx

Answer 5

np :)

Answer 6

use partial fractions for this one so you'll have the following form:\[= (A/x^2 + 1) + (B/x+7)\]

try it out ^_^

Answer 7

and after that you plug in the value right?

Answer 8

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 ^_^

Answer 9

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

Answer 10

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

Answer 11

thanks you are a BIG HELP!

Answer 12

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

Answer 13

\[\int\limits_{0}^{1} \ln(x) / x ^{1/2} dx \]

to approximate this integral using the trapezoid rule.

if you can help me with this one also, i am sorry :(