Eveluate the integral how to d

As follows:

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2010-01-09 14:00:13 補充：
We use the substitution x=(3/2)tanθ in step 2. We use it here because of the trigonometric identity: tan²θ+1=sec²θ

2010-01-09 14:00:19 補充：
Since "dx" involves secθ and so does the denominator, then we can simplify the integration into ∫dθ, the question is a lot simpler than the original one.
Finally, express the ans in terms of x...

2010-01-09 14:00:26 補充：
Instead of calculating it, we can simply apply the formula: ∫dx/(x²+a²)=(1/a)arctan(x/a)+c to find the answer.

2010-01-09 14:01:06 補充：
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