Partial Fractions Q10 (2 Viewers)

[want2beSMART]

INTEGRAL of xdx/(x+1)(x^2+9)

 

[KFunk]

x = a(x² +9) + (bx +c)(x+1)
= (a+b)x² + (b+c)x + 9a + c

a+b=0
b+c=1
9a+c=0

solve simultaneously and a= -1/10, b= 1/10, c=9/10 so you get:
1/10 ∫ x/(x² +9) + 9/(x² +9) - 1/(x+1) dx

= 1/10[(1/2)ln(x² +9) + 3tan^-1(x/3) -ln(x+1)] + C

 

[3.1415926535897]

have u learnet partial fractions yet...

cos that is like the first q's u do...

 

[want2beSMART]

its seems obvious that i havent