Methods of Integration (Step-by-Step Learning)

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🔧 Common Methods of Integration

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1. Substitution Method

$\int 𝑓(𝑔(𝑥)){𝑔}^{\mathrm{\prime }}(𝑥)𝑑𝑥=\int 𝑓(𝑢)𝑑𝑢$

👉 Used when function is inside another function.

Example idea:
If $𝑢=𝑔(𝑥)$, then solve easily.

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2. Integration by Parts

$\int 𝑢𝑑𝑣=𝑢𝑣-\int 𝑣𝑑𝑢$

👉 Used when two functions are multiplied.

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3. Standard Integrals

$\int \sin 𝑥𝑑𝑥=-\cos 𝑥+𝐶$

$\int {𝑒}^{𝑥}𝑑𝑥={𝑒}^{𝑥}+𝐶$

👉 These are formulas you must remember.

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📊 Tips for Students

• Practice daily
• Learn formulas properly
• Understand steps, don’t memorize blindly
• Solve previous year questions

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🧾 Conclusion

Different methods of integration help solve different types of problems. With practice, you can easily decide which method to use.