Integral calculus
The indefinite integral
Binomial integral
Solving binomial integrals examples
Binomial integral
Integral of the form
is called the binomial integral where, a and b are real numbers while m, n and p are rational numbers.
If  m, n and p all are integers then the integrand is a rational function integration of which is shown above.
There are only three cases the binomial integral can be solved by elementary functions:
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.
2.  if  p is a fraction and  (m + 1) / is an integer, then the integral can be solved using substitution
a + bxn = t s,  where  s  is denominator of  p.
3.  if  p is a fraction and  (m + 1) / n + is an integer then, the integral can be solved using substitution
ax - n + b = t s,  where  s  is denominator of  p.
Solving binomial integrals, examples
 Example:  82. Evaluate
 Solution:
 Example:  83. Evaluate
 Solution:
 Example:  84. Evaluate
 Solution:
Calculus contents F