Basic Laws of Integration
Let f(x) and g(x) be any two functions of x, then
ExampleSolution

ExampleSolutionGiven
Some More Standard Results
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Note: e^{log f (x) }= f (x)
Example
Evaluate
Solution
We know that
Example
Evaluate
Solution
We know that
Example
Evaluate
Solution
Example
Solution
Integration by Substitution
Let be a given integral. Sometimes it is not possible to be able to integrate f (x) directly. We can substitute f (x) into some other function g(t) to make it readily integrable.
Let f (x) = g(t) be another function.
Example
Solution
We can see that 1/x is the derivative of log x. So, we can easily use substitution here.
Let log x = t
Differentiating both sides with respect to x, we get
Let log x = t
Differentiating both sides with respect to x, we get