In this problem, we are going to use five different ways to solve the following indefinite integral: I= int (dx)/(x sqrt(x^(2)-1)) You will get five different answers by using these five methods. This is normal in computing indefinite integrals since they are represented by any antiderivative of the integrand plus a constant. Because the choice of solutionspile.com

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In this problem, we are going to use five different ways to solve the following indefinite integral:

I=\int (dx)/(x\sqrt(x^(2)-1))

You will get five different answers by using these five methods. This is normal in computing indefinite integrals since they are represented by any antiderivative of the integrand plus a constant. Because the choice of antiderivatives is arbitrary and any two antiderivatives differ only by a constant, it's possible to see that different methods produce different representations of the antiderivatives. Hint: notice that the domain of your integrand is

(-\infty ,-1)\cup (1,\infty )

. In some parts, you may need to consider the two different cases:

x>1

and

x<-1

. (d) Use the

u

-sub with

u=x-\sqrt(x^(2)-1)

to compute this integral. (e) Use the

u

-sub with

u=(x-1)/(\sqrt(x^(2)-1))

to compute this integral.

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