want2beSMART
Artificial Happiness c[x
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INTEGRAL of xdx/(x+1)(x^2+9)
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Partial Fractions Q10 (1 Viewer)
- Thread starter want2beSMART
- Start date
x = a(x<sup>2</sup> +9) + (bx +c)(x+1)
= (a+b)x<sup>2</sup> + (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/(x<sup>2</sup> +9) + 9/(x<sup>2</sup> +9) - 1/(x+1) dx
= 1/10[(1/2)ln(x<sup>2</sup> +9) + 3tan<sup>-1</sup>(x/3) -ln(x+1)] + C
= (a+b)x<sup>2</sup> + (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/(x<sup>2</sup> +9) + 9/(x<sup>2</sup> +9) - 1/(x+1) dx
= 1/10[(1/2)ln(x<sup>2</sup> +9) + 3tan<sup>-1</sup>(x/3) -ln(x+1)] + C
3.1415926535897
Pi Pi Pi Pi Pi Pi Pi Pi!!
- Joined
- Mar 20, 2005
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have u learnet partial fractions yet...
cos that is like the first q's u do...
cos that is like the first q's u do...
want2beSMART
Artificial Happiness c[x
- Joined
- Nov 2, 2004
- Messages
- 441
- Gender
- Male
- HSC
- 2005
its seems obvious that i havent