Question Number 149241 by john_santu last updated on 04/Aug/21

Answered by ajfour last updated on 04/Aug/21

s=∫_0 ^( 1) ((x^3 dx)/((x−1)^3 +(3−h)(x−1)+hx)) 3−h=5 ⇒ h=−2 s_1 =∫((x^3 dx)/((x−1)^3 +5(x−1)−2x)) s_2 =∫(((1−x)^3 dx)/(−x^3 −5x−2(1−x))) =∫(((x−1)^3 dx)/(x^3 +5x−2(x−1))) =∫(((x−1)^3 dx)/(x^3 +3x+2)) trying factors of d^r one is p=(((√2)−1))^(1/3) −(((√2)+1))^(1/3) s =∫_0 ^( 1) (((x−1)^3 dx)/((x−p)(x^2 +qx+r))) we′ll employ partial fractions.

Answered by john_santu last updated on 04/Aug/21