How do you evaluate #\int e ^ { x } \sqrt { 9+ 2e ^ { x } } d x #?
2 Answers
Explanation:
This isn't as bad as it looks, actually!
The first thing we can do is recognize that
So our original equation turns into
U-Substitution seems to be the best way to go.
Our
So,
We have
Let's solve for that, then.
Now that we have
You should immediately see the
We can take the
Now it looks much easier. (I hope)
The power rule tells us how to solve this.
Remember:
Following that, we can solve our equation.
Simplifying this, our final answer is
Right?
Wrong!
Don't forget to substitute the real value for
Our final answer is:
You can check the answer by finding its derivative.
Explanation:
we can do this by inspection
the outside is a constant multiplied by the derivative of the bracket, suggesting the integral is the bracket to the power +1
try
by the chain rule we have
comparing with the integral we have