For 

,

first substitute 

.

Replace u with :

.

To integrate this expression, use u substitution. Assign . Now, you can substitute everything in: . Remember that when integrating a single variable on the denominator, the integral is ln of that term. After integrating, you get: . Substitute the original expression back in and add a +C because it is an indefinite integral:

To integrate this expression, use u substitution. Assign . Everything can be substituted, so now rewrite: . Remember that when there is a single variable on the denominator, the integral is ln of that term: . Substitute back in your initial expression: . Now, evaluate at 3 and then 1. Subtract the results:

To integrate this expression, you must use u substitution.

Assign

.

Now everything can be substituted in.

The new integration problem looks like this:

.

Remember that when there is a single variable on the denominator, the integral is natural log of that term.

After integrating, you should get

.

Then substitute back in your original expression and add a +C because it is an indefinite integral:

To integrate this expression, use u substitution.

Assign

.

Since everything can be substituted, rewrite the problem:

.

The integral of is .

Therefore, after integrating, you get: . Then, substitute your original expression back in to get .

Remember to add a C because it is an indefinite integral. Your final answer is:

.

We first rewrite the function

To solve the indefinite integral, we set .

Deriving then gives the equation , or . Substituting in for  and  gives the integral

Finding the anti derivative of this function we get

and replacing  yields the answer

To integrate, we must first make a substitution:

The derivative was found using the rule

Now, we can rewrite the integral in terms of u, and integrate:

The integral was found using the following rule:

Finally, replace u with our original x term:

First, assign u substitution in order to integrate the expression:

Now, substitute everything in so you can integrate:

Now, integrate. Remember when there is a single x on the denominator, the integral is ln of that term.

Now, substitute back in the initial expression and add a +C because it is an indefinite integral:

To integrate this expression, you'll have to use u substitution. Assign your "u."

Now, substitute everything in:

Integrate:

Substitute your original expression back in and add a C because it is an indefinite integral:

To solve this integral, we use u substitution. However, to do so, we must break our integral into two separate integrals, which looks like this:

Now that we have two separate integrals, we can make the appropriate substitutions for each one. For the first integral, we make the following substitution:     . For the second integral, we make this substitution:   . This changes our integral to: , which equals:. Plugging back in our respective values for u and v, we get:

 .