Problem solving tips

Integrals

- Tips and Tricks you'll need to solve the problems
1
Tip: While integrating functions if an integrand contains a function within a function. For example . Use substitution, we have within function, substitute another variable (say u) for the internal function and change variable of integration.
is equal to
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None of these
2
Tip: Rational functions of the form can be expressed as sum of fractions with linear or quadratic functions in their denominator (partial fractions). So while integrating rational functions, write them partial fractions and find out the values of constants in the numerator to integrate the function easily.

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3
Tip: When integrating functions of the type , use product rule of integration, = . Choose based on order Inverse trigonometric, logarithmic, algebraic, trigonometric and exponential functions (ILATE).

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D
4
Tip: If an integrals of the type , , , . Use trigonometric substitution as given the table to eliminate the and then find the integral of the given function.
 Integral contains this form Try this substitution or or
then
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5
Tip: If the integrals involve only sine and cosine functions raised to odd power (say x and y), rewrite or as cosine or sine remaining function. Use identities or and then apply substitution method.
Evaluate :