Evaluate: `int(x^2+4x)/(x^3+6x^2+5)\ dx`

Explanation

Solution:

Given,

`\int(x^{2}+4 x\right) /(x^{3}+6 x^{2}+5) d x`

Let `t=x^{3}+6 x^{2}+5`

`\Rightarrow d t=(3 x^{2}+12 x) d x`

`\Rightarrow d t=3(x^{2}+4 x) d x`

`\Rightarrow \frac{1}{3} d t=(x^{2}+4 x) d x`

Now,

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