|
Multiply out the inside and complete the square to get
6.25-(x-0.5)2 (= (2.5)2 - (x-0.5)2.) Then
either trig sub or sub to use the table.
|
|
Substitute: w = sqrt(x). (Note: Sometimes people will write this as
w2 = x, so that getting 2w dw = dx is real easy. ) Then use
integration by parts.
|
|
Either use substitution with w = x2+1, then partial fractions,
OR, use trig sub (then the whole integrand can be made sec(t), with dx =
-csc2(t), then sub, then partial fractions. The second method
is longer, but it has the advantage of feeling straightforward the whole
time. As always, use the one with which you're more comfortable.
|
|
Use trig sub with the hypotenuse being 3x and one of the legs being
1.
|
|
Do long division first, then complete the square on the bottom to get
(x+3)2+52 (on the bottom)!, then substitute w = x+3
so that you can use the table.
|