evaluate the definite integral [0,1] of ln(4+x^2)dx

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You should use integration by parts such that:

`int udv = uv -  int vdu`

Considering `u=ln(4+x^2)`  and `dv = dx`  yields:

`u=ln(4+x^2) => du = (2x)/(4+x^2)`

`dv = dx => v= x`

Using the formula of integration by parts yields:

`int ln(4+x^2) dx = xln(4+x^2)- int (2x^2)/(4+x^2)dx`

`int ln(4+x^2) dx = xln(4+x^2)- 2int (x^2)/(4+x^2)dx`

You need to evaluate `int (x^2)/(4+x^2)dx` , hence, you...

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