Question

evaluate integral of x^2/(x^2+4)(x^2+9) dx​

Answer 1

Answer:

-2/5 tan⁻¹ ( x/2 ) + 3/5 tan⁻¹ ( x/3 ) + c

Step-by-step explanation:

To find----->

∫ x² dx / ( x² + 4 ) ( x² + 9 )

Solution---->

1) Plzz refer the attachment

2) First we do partial fraction for this we put

x² = y , in it we get,

x² / ( x² + 4 ) ( x² + 9 )

= - 4 / 5 ( x² + 4 ) + 9 / 5 ( x² + 9 )

3) Then we integrate it by using formula of integration ,

∫ dx / ( x² + a² ) = 1 / a tan⁻¹ ( x / a ) + C

Additional information----->

1) ∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C

2) ∫ dx / x = logx + C

3) ∫ eˣ dx = eˣ + C

4) ∫ aˣ dx = aˣ / loga + C

5) ∫ Sinx dx = - Cosx + C

6) ∫ Cosx dx = Sinx + C

7) ∫ Sec²x dx = tanx + C

8) ∫ Secx tanx dx = Secx + C

9) ∫ Cosec²x dx = - Cotx + C

10) ∫ Cosecx Cotx dx = - Cosecx + C

Answer 2

Answer:

i hope it helps.............