integration problem please explain steps?

it will be easier if u make it in this form

(2x+2)/2(x^2 +2x+5) + 3/((x+1)^2 +4)

the first one u can solve it by changing variables where u take

u= x^2 +2x+5 u will get the integral of du/u = lnu

and the second one 3/4 [1/ ((x+1)/2)^2 + 1]

here u can change the variable putting u=(x+1)/2

u will get the intregral of du/(u^2 +1)= inverse tan u

but beware of constants

It's actually not a partial fractions problem because the denominator cannot be factored. Instead, complete the square in the denominator, break into two pieces and integrate each piece separately. Since the denominator is (x+1)^2+4, one piece on the top should be x+1.

integration for these kind of questing is all about sub of U

change the denomanator into (x^2 + 2x +5)^-1 then let

U=(x^2 + 2x +5)

so du=2x+2

x+4 dx = (x+4)/(2x+2) du

so :Int (x^2 +2x +5)^-1 du

do the sub of u and ull get the answer..but when u try to

Int U^-1 it ll be undefined so try to manipulate the fraction.

first convert the numerator into x/(x^2+2x+5) +4/(same) and integrate them individually applying special integrals,which must be given in ur book.

the by-made from place is speed, and so the crucial of speed is place. in case you combine the speed function from a to b, then you definately get the finished distance traveled from time a to time b. crucial sint = -fee. evaluated from 0 to pi/2 = -cos(pi/2) - -cos(0) = 0 - -a million = a million crucial fee = sint. evaluated from pi/2 to 2pi = sin(2pi) - sin(pi/2) = 0 - a million = -a million. i think of you have the bounds incorrect for area b.