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The substitution method for solving integrals involves substituting a new variable in place of the original variable in the integral. This new variable should be chosen in a way that simplifies the integral and makes it easier to solve. After substitution, the integral can be solved using basic integration rules.
Integration by parts is a technique used to solve integrals that are products of two functions. It involves rewriting the integral using the product rule, and then rearranging the terms to solve for the integral. This method is useful for integrals that cannot be solved using basic integration rules.
Partial fractions is a method used to simplify integrals that contain rational functions. The first step is to express the rational function as a sum of simpler fractions. Then, each fraction can be integrated separately using basic integration rules. The final step is to combine the individual integrals to get the solution for the original integral.
Integrals involving trigonometric functions can be solved using trigonometric identities and substitution. The substitution method involves choosing a new variable that will make the integral easier to solve. Trigonometric identities can also be used to simplify the integral and make it more manageable.
Improper integrals are integrals with infinite limits of integration or integrals with discontinuous integrands. These integrals cannot be solved using basic integration rules. Instead, they are solved using the limit definition of the integral, where the limits of integration are taken to infinity or the points of discontinuity are approached from both sides.
