what r the possible methods to integrate a functions.which are included in iitjee.

Those are different integration techniques that are useful in different situations, depending upon what the form of your function being integrated is. I would recommend going back to you calculus text and looking up in what context each technique was introduced:

A summary would be:

1. Substitution: obviously useful when your integrand (the function being integrated) is actually the derivative of composition of two functions i.e. it has the form of something that has been differentiated using the chain rule.

2. By parts: useful when your integrand looks like one of the terms of something that has been differentiated using the product rule.

3. Trigonometry. This should be obvious! If your integrand has trigonometric functions, then it is applicable, otherwise it isn't.

4. Partial fractions: Umm...again fairly self explanatory. If I recall correctly, this is useful if your integrand can be decomposed using partial fractions.

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