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in Indefinite Integral by (33.4k points)
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Evaluate : \(\int\frac{x^2}{(x^2+4)(x^2+9)}dx\)

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Let I = \(\int\frac{x^2}{(x^2+4)(x^2+9)}dx\)

Put x2 = t, we get

∴ \(\frac{x^2}{(x^2+4)(x^2+9)}\)

\(\frac{t}{(t+4)(t+9)}\)

Now,

\(\frac{t}{(t+4)(t+9)}\) = \(\frac{A}{(t+4)}+\)\(\frac{B}{(t+9)}\)

\(\frac{A(t+9)+B(t+4)}{(t+4)(t+9)}\)

⇒ t = (A + B)t + (9A + 4B)

Equating the coefficients, we get

A + B = 1,

9A + 4B = 0

Solving above two equations, we get

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