Name: Jim

Who is asking: Student
Level: Secondary

Question: I'm having trouble with these integrals. Can you help me out?

1)the integral of:

x⁵ arctan x dx

2)the integral of:

2x⁵ + 9x⁴ + 19x³ + 13x² - 5x - 25
-----------------------------------------------  dx
       x⁴ + 4x³ + 5x²

For 2) divide the denominator into the numerator to get a polynomial plus a rational expression where the degree of the numerator is less than the degree of the denominator. This rational expression can then be integrated using partial fractions.

For 1) integration by parts, with u = arctan(x), dv = x⁵ produces a rational function that you can handlel as in part a).

Once you have completed the problems you can check your results using "The Integrator", at http://integrals.wolfram.com/index.cgi (When using the integrator for 2) the notation is x^5 ArcTan[x].)