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Evaluate: int(x^2+1)/((x^2+4)(x^2+25))\ ...

Evaluate: `int(x^2+1)/((x^2+4)(x^2+25))\ dx`

Text Solution

Verified by Experts

Let `I=int frac{x^{2}+1}{(x^{2}+4)(x^{2}+25)} d x`
We express
`frac{x^{2}+1}{(x^{2}+4)(x^{2}+25)}=frac{A x+B}{x^{2}+4}+frac{C x+D}{x^{2}+25} `
`Rightarrow x^{2}+1=(A x+B)(x^{2}+25)+(C x+D)(x^{2}+4)`
Equating the coefficients of `x^{3}, x^{2}, x` and constants, we get
`0=A+C` and `1=B+D` and `0=25 A+4 C` and `1=25 B+4 D`
or `A=0` and `B=-frac{1}{7}` and `C=0` and `D=frac{8}{7}`
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