# Basic Laws of Integration

Let f(x) and g(x) be any two functions of x, then

1.
where c is any constant

Example
Solution

2.

Example
Solution
Given

Here ee is a constant.

# Some More Standard Results

 1 2 3 4 5 6 7 8 9 10 11 12

Note: elog f (xf (x)

Example
Evaluate
Solution
We know that

Example
Evaluate
Solution
We know that

Example
Evaluate
Solution

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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