Question

need help with an integral :)

Answer 1

\[\int\limits_{}^{}(1-x^2)\sqrt{1+4x^2}dx\]

Answer 2

I'm stuck on this one :(

Answer 3

i think you should let 2x = tan(theta) --> x = tan(theta)/2 and (2x)^2= tan^2(theta)
---> 1+(2x)^2= 1+tan^2(theta)= sec^2(theta). take sqr(sec^2(theta))=sec (theta)
you have sqr part done at sec(theta)

Answer 4

now, with 1-x^2, you can do this 2x=tan(theta)as above, x =tan(theta)/2---> x^2 = tan^2(theta)/4 and 1- tan^2(theta)/4. don't forget take dx = sec^2(theta)d(theta)/2. combine everything together, it is easy to get the answer