Question

Evaluate the indefinite integral. (Remember to use ln |u| where appropriate.)http://www.webassign.net/cgi-bin/symimage.cgi?expr=int%20x%2A%2A%2811%29%2F%28x%2A%2A%2812%29%20%2B%204%29text%28%20%29%20dx

Answer 1

You're going to do this by u-substitution. Let u=x^12+4. You get du=x^11dx
\[\int\limits\limits_{}^{}\frac{x^{11}}{x^{12}+4}dx=\int\limits \frac{du}{u}=\ln|u|+C=\ln|x^{12}+4|+C\]

Answer 2

ok and x^11 = 11x^10

Answer 3

You don't need to integrate that part. Take the derivative of x^12+4, and the x^11 will appear as part of the chain rule. u-substitution accounts for the chain rule. You won't need to integrate x^11 separately.

Answer 4

Oops, I meant "Take the derivative of ln(x^12+4)..."

Answer 5

ok and x^11 = 11x^10

Answer 6

12x^11

Answer 7

Nah, still don't need it.