Evaluate:∫2x/(x^2 + 1)(x^2 + 3)dx ​

Question

Evaluate:

\(\int\frac{2x}{(x^2+1)(x^2+3)}dx\)

∫2x/(x² + 1)(x² + 3)dx

Answer 1

Let I = \(\int\frac{2x}{(x^2+1)(x^2+3)}dx\)

Put t = x² 

dt = 2xdx

A(t + 3) + B(t +1) = 1 

Putting t + 3 = 0, 

X = -3 

A(0) + B(- 3 +1) = 1

B = - 1/2

Putting t +1 = 0, 

X = -1 

A(- 1 + 3) + B(0) = 1

A = 1/2

From equation(1),we get,