- #1
limelightdevo
- 5
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Homework Statement
Integral, from 4 to 6, 1/(t^2-9) dt
Homework Equations
please use my approach to solve it, like with cosh and whatnot
The Attempt at a Solution
Integral, from 4 to 6, 1/(t^2-9) dt
so I multiplied the top and bottom by square root of 9.
which got me square root of (t/3)^2 - 1 in the denominator.
so I got integrated that into arccosh (t/3) - arccosh (t/3) from 4 to 6
after some solving, it came down to square root of 9 times ((ln(2)+squareroot3))-(ln(4/3)+squareroo… And that is where I got stuck. If I distribute in the square root 9,it should be (3 ln(2) + square root 3) - (3 ln (4/3) + square root (7/9)), which results in (ln 8 + 3*square root 3) - (ln (4/3)^3 + 3*square root (7)). But when I distribute the square root 9 in and when it multiplies with ln(2), for example, it should be ln 2^3 and not ln 2*3 based on the multiplication rule of natural log. But by doing the wrong way, it perfectly leads to the answer, which is ln(6+3*square root 3)/(3+square root 7)
Please help
Thankssss