This integral can most easily be done by u-substitution.  Begin by rewriting the integral as

. 

Choose , therefore

.

This integral can be evaluated by using u-substitution.  Choose 

.  This means

.

In order to integrate, we will need to expand the binomial.  Substitution will not work since there is no valid  term to replace  if we let .

Expand the binomial.

The integral becomes:

Integrate each term.

The answer is:  

Use substitution to solve this question.

Let , and by adding three on both sides, and we have .

Take the derivative of u with the respect to x.

With the three equations, we can substitute the integral in terms of u.

Rewrite the denominator as , and separate the integral into two integrals.

Integrate the terms separately.

Add the two integrals.  The constants can be combined as a single constant at the end.

We can also pull out a  as a common factor.

Substitute  back into the answer.

Simplify the terms in the bracket.

The fractional exponent of one-half is a square root of the quantity.

The answer is:  

Step 1: Find the integration of each term:







Step 2: Re-write the function in terms of the integrated terms:



Step 3: Find the upper limit:

Step 4: Find the Lower Limit:

Step 5: Subtract the upper limit and the lower limit:

We will be using integration by parts for this problem

To integrate, we can change the integrand using the double angle formula to something we can integrate:

Next, we make a substitution:

The derivative was found using the rule

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

We used the following integration rules:

, 

Finally, replace u with our original x term:

To integrate, we must integrate by parts, using the formula

We now designate our u and dv, and differentiate and integrate, respectively:

The rules used are as follows:

, 

Next, we use the above formula:

Finally, integrate:

The following rule was used to integrate:

The integrand can be simplified to make the problem much easier to solve. You must use the fact that  in order to rewrite the integrand. After rewriting, the problem is now:

Here, a simple u-substitution can be used:

, , 

Once again, the integrand can be rewritten with values of u:

The integral was taken by using the following rule:

Once u has been replaced with x, the final answer is:

There are no apparent substitutions to simplify the integrand, but you can rewrite it as:

With this expression, it s clear that you must solve the integral by using partial fractions. To do this, two fractions must be created that add up to the integrand. Specifically, the partial fractions will be:

Next, the denominator must be cleared in order to solve for the unknowns. To do this, the entire equation must be multiplied by a common denomionator, . The resulting equation is:

Next, a system of equations must be created by equating the coefficients of the terms with the same power of x. The result is:

After solving, you find that 

With these values found, they can be plugged back into the original equation and integrated:

The final answer is:

The integrals were evaluated by using the following rule: