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Substitute w = sqrt(s); then use partial fractions
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Complete the square so that the inside of the square root is 1 -
(x-1)2; Then either substitute or guess/check (it should be
arcsin(x-1)!)
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Substitute w = arcsin(x) (antiderivative should then be
(1/2)(arcsin(x))2
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Rewrite cos3(x) = cos(x)(1-sin2), then substitute
w = sin(x).
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Either rewrite sec3(x) as 1/cos3(x), then use
the table, OR do boomerang integration by parts, with u = sec(x), dv =
sec2(x).
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Use integration by parts, with u = ln(**stuff**), dv = du. Be careful
when finding du!
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New Ones Below!
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Substitute w = et + 1; this turns it into the first integral
of this page!
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If the term on the outside was ex, we could substitute, then
use integration by parts; as it stands, we (probably) have to approximate
it numerically.
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Substitute: w = x2+1; the integrand then becomes
0.5(w-1)/w2, then rewrite... .
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Substitute: w = e2t+1. The integrand then becomes
0.5(w-1)/w2/3; (in other words, it's almost identical to the previous
problem.)
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