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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:

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:

 

General Contents

Detailed Contents

Index