Definite Integral of the reciprocal of a radical times a power: ![]()
As usual, we need to convert the radicals to powers in the numerator:

Notice how the exponent in the parentheses does not change.
Now we can try a substitution:
Let
, and
. We can use this to evaluate the indefinite integral,
, using the power rule for integration:
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Now we can substitute to get an expression in terms of x:
.
Finally, we can apply the Fundamental Theorem of Calculus to get the required definite integral:
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