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| Integral
calculus |
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The
indefinite integral |
Binomial
integral
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Solving
binomial integrals examples
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Binomial
integral
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Integral
of the form
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is
called the binomial integral where, a
and b
are real numbers while m,
n
and p
are rational numbers.
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If
m,
n
and p
all are integers then the integrand is a rational function
integration of which is shown above.
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There
are only three cases the binomial integral can be solved by
elementary functions:
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1. if m
and n
are
fractions and p
is an integer then, the integral can be solved using
substitution x
= t s, where
s
is the least common denominator of m
and n.
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2. if p
is a fraction
and (m +
1) / n is an
integer, then the integral can be solved using substitution
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a + bxn = t s,
where s
is denominator of p.
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3. if p
is a fraction
and (m +
1) / n + p
is an integer then, the integral can be solved using substitution
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ax - n
+ b = t s,
where s
is denominator of p.
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Solving
binomial integrals, examples
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| Calculus contents
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