The two forms are equivalent, as you may write:
Since in a constant, it may be combined with the constant of integration.
Integral of:
I completed the square on the denominator to rewrite it as:
When I try to solve this, I let:
So we get the integral of:
Then I set:
This simplifies to just the integral of:
The integral of this is:
When I setup a right triangle, I get the following sides:
Hypotenuse:sqrt((x+1)^2+64)
Adjacenet: 8
Opposite: x+1
When I use these values to replace tan(theta) and sec(theta) my final answer is:
However, the online website has a different answer. It has the same basic terms but without dividing by 8. Where am I going wrong?
Hello, vesperka!
Your final line should have a Plus (+).
However, the online website has a different answer.
It has the same basic terms but without dividing by 8.
Where am I going wrong? . Your answer is correct!
They did some "invisible" (very sneaky) simplifying.
You had: .
. . . . . .
. . . . . .
. . . . . .
Yes . . . just one more thing to watch for.
Thanks for the replies guys. I didn't realize this, but for the integral of sec(theta) I was multiplying the tangent and secant inside of the natural log when they actually should be added together. Thanks for the explanation on why -ln(8) is a constant that can be factored out!