# Integration by Substitution

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7) Determine the integral (square root of 9x^2 + 4) /x^4 dx

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7)determine the integral (square root of 9x^2 + 4) /x^4 dx

We will use substitution method to evaluate the integral.

Let

And

Substituting to the above integral:

Where c is integration constant.

Now we need to find sinu in terms of x

We used the substitution

In the following right triangle, we use x and 2/3 as the two sides. Then

The hypotenuse is

And

Substituting sinu to the integral result gives

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