Hint :
Substitute
Result should be :
Hi. Using trig sub to get integrals, I keep getting different but possibly equivalent answers as in book, and on calculator.
For example, integral(5/sqrt(25x^2-9),x)
By trig sub,
I get: ln|5x/3+(5sqrt(x^2-9/25)/3|+c
Calculator gets: ln(sqrt(25x^2-9)+5x)
Wolfram integrator gets: log(2(sqrt(25x^2-9)+5x))
But, I am pretty sure I did the problem correctly.
Are they equivalent? If they are, How can I show that they are to avoid my teacher marking off points?
Thats what I did.
The integral simplifies first to integral(1/sqrt(x^2-9/25),x)
x=(3/5)*sec(u)
...
In the end it is integral(sec(u),u)
=ln|sec(u)+tan(u)|+c
I have a right triangle, where hypotenuse is x, opposite is sqrt(x^2-9/25), and adjacent=3/5.
So, sec(u)=1/((3/5)/x)=5x/3, and tan(u)=sqrt(x^2-9/25)/(3/5)=sqrt(25x^2-9)/3.
So I get: