can someone help me with this problem 2x/Sqrt(1+x^4) Thank you.
L link88 New member Joined Nov 29, 2008 Messages 1 Nov 29, 2008 #1 can someone help me with this problem 2x/Sqrt(1+x^4) Thank you.
F fasteddie65 Full Member Joined Nov 1, 2008 Messages 360 Nov 29, 2008 #2 Re: indefinite integral ? 2x/sqrt (1 + x^4) Let u = x^2 du = 2x dx ? 2x/sqrt (1 + x^4) dx = ? du/sqrt(1 + u^2) Now, let u = tan ø and du = sec^2 ø dø ? 2x/sqrt (1 + x^4) dx = ? du/sqrt(1 + u^2) = ? sec^2 ø dø/(sqrt(1 + tan^2 ø) = ? sec^2 ø dø/sqrt(sec^2 ø) = ? sec^2 ø/sec ø = ? sec ø dø = ln |sec ø + tan ø| + C = ln |sqrt (1 + u^2) + u| + C = ln (sqrt (1 + x^4) + x^2) + C
Re: indefinite integral ? 2x/sqrt (1 + x^4) Let u = x^2 du = 2x dx ? 2x/sqrt (1 + x^4) dx = ? du/sqrt(1 + u^2) Now, let u = tan ø and du = sec^2 ø dø ? 2x/sqrt (1 + x^4) dx = ? du/sqrt(1 + u^2) = ? sec^2 ø dø/(sqrt(1 + tan^2 ø) = ? sec^2 ø dø/sqrt(sec^2 ø) = ? sec^2 ø/sec ø = ? sec ø dø = ln |sec ø + tan ø| + C = ln |sqrt (1 + u^2) + u| + C = ln (sqrt (1 + x^4) + x^2) + C
