Integrate the function:


Given:


Using partial differentiation:


let



5x=A(x2+9)+(Bx+C)(x+1)


5x = Ax2 +9A+ Bx2 +Bx+ Cx + C


5x = 9A + C + (B+C)x + (A+B)x2


Equating the coefficients of x, x2 and constant value. We get:


(a) 9A + C = 0 C = -9A


(b) B+C = 5 B = 5-C B = 5-(-9A) B = 5 + 9A


( c) A + B =0 A = -B A = -(5 + 9A) 10A = -5 A = -1/2


and C = 9/2 and B = 1/2


Put these values in equation (1)










Put x2 = t 2xdx = dt





Put the value in equ. (2)



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