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# 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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 7, 2022, 6:08 pm ad1c9bdddf>
https://brainmass.com/math/integrals/integration-substitution-170536