Calculus Examples

Divide by .
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Factor the numerator and denominator of .
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Write as .
Simplify.
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Remove parentheses around .
Let . Then . Rewrite using and .
The integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Let . Then . Rewrite using and .
The integral of with respect to is .
Simplify the answer.
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Simplify.
Replace all occurrences of with .
Replace all occurrences of with .
Simplify each term.
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Simplify by moving inside the logarithm.
Remove the negative exponent by rewriting as .
Use the product property of logarithms, .
Simplify the log argument.
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Write as a fraction with denominator .
Multiply and .
Simplify by moving inside the logarithm.
Apply the product rule to .
Simplify the numerator.
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Multiply the exponents in .
Simplify.
Simplify the denominator.
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Rewrite.
Multiply the exponents in .
Simplify.
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