To integrate, the following substitution is made:

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

The integral was performed using the following rule:

Finally, replace u with the original term (containing x):

To integrate, we must perform the following substitution:

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

The integral was performed using the identical rule (the constant in front doesn't change the integral). 

Finally, rewrite the result in terms of x:

To integrate, we can split the integral into two integrals:

The first integral is equal to 

and was found using the following rule:

The second integral can be made easier with the following substitution:

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

The integral was performed using the identical rule.

Next, we rewrite our answer in terms of x, and add it to the first integral's result, combining the two integration constants into a single one:

To integrate, we can split the integral up (the property of linearity allows us to do this):

The first integral is equal to

and was found using the following rule:

The second integral can be solved after the following substitution is made:

Rewriting the integral in terms of u and integrating, we get

The integral was solved using the identical rule.

Next, rewrite the answer in terms of x:

Finally, add this to the first result to get our final answer:

Note that all of the integration constants were combined to make a single constant. 

To integrate, the following substitution must be made:

The following rule was used to find the derivative:

Next, rewrite the integral in terms of u and integrate:

The integral was performed using the identical rule. 

Finally, rewrite the integral in terms of x by replacing u:

To integrate, the following substitution must be made:

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

The following integration rule was used:

To finish, we replace u with our original x term:

First we distribute the  which will allow us to break the integral up into two parts.

.

For the first integral, we use substitution of variables. Letting , we find that  or that . Substituting these two equations in, we have 

At this point, you can use the formula for integrating exponentials, or just recall the simple derivation for it

The second integral is simple power rule.

Combining these two expressions and substituting back in for u, we get a final answer of

Note, if you didn't distribute the  at the beginning, this is fine. Substitution of variables will still work correctly. Just be careful that when you integrate  you remember that this becomes u, and not x. The extra -8 you get when doing this can just be combined with the C term.

To integrate, the following substitution was made:

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

The following rule was used to integrate:

Finally, rewrite the answer in terms of x:

To integrate, we must make the following substitution:

Rewriting the integral in terms of u and integrating, we get

The integral was performed using the identical rule.

Finally, replace u with the original x term:

Use substitution to solve the integral

Rewrite the integrand as a negative exponent: 

Therefore: 

Make the following substitution:    

Apply the substitution to the integrand: 

Solve the integral: 

Re-substitute the value of u: 

Solution: