Indefinite Integration

Integration By Substitution – Formula and Examples

Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If \(\phi(x)\) is continuously differentiable function, then to evaluate integrals of the form \(\int\) …

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Integration Examples

Here you will learn some integration examples for better understanding of integration concepts. Example 1 : Evaluate : \(\int\) \(dx\over {3sinx + 4cosx}\) Solution : I = \(\int\) \(dx\over {3sinx + 4cosx}\) = \(\int\) \(dx\over {3[{2tan{x\over 2}\over {1+tan^2{x\over 2}}}] + 4[{1-tan^2{x\over 2}\over {1+tan^2{x\over 2}}}]}\) = \(\int\) \(sec^2{x\over 2}dx\over {4+6tan{x\over 2}-4tan^2{x\over 2}}\) let \(tan{x\over 2}\) = …

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