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Substitution: w = x2 + 1.
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Partial fractions (or table): The bottom factors into (x-3)(x-4), so
rewrite the fraction as -7/(x-3) + 9/(x-4), then it's easy...
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Do boomerang or table
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It's probably easiest if you break the integrand into two fractions:
one with 3x on top (which you'd do by substitution) and one with 2 on top
(which we recognize as the derivative of 2arcsin(x))..
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Break into the sum of two integrals: To find the antiderivative of
sec(x/3), substitue w = x/3, then know the antiderivative of sec(w). to do
the other, try substitution with w = sqrt(x), then partial fractions (or
table.)
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