Learn How To Integrate Sin X

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# How to integrate sin x?

We will use integration by substitution to integrate sin x.

## Answer: The final integral of sin x is − cos x + C

Go through the explanation to understand better.

**Explanation:**

To solve ∫ sin x dx, let sin x = u ⇒ cos x dx = du

By trigonomteric identity: cos^{2}x = 1 - sin^{2}x, we get

⇒ dx = du / cos x = du / √(1 − u^{2})

∫sin x dx = ∫u (du / √(1 − u^{2}))

= ∫u (1 − u^{2}) ^{-1/2 }du

= −1/2 ∫(1−u^{2})^{-1/2}. (−2u) du

= −1/2 √(1 − u^{2})/(1/2) + C

= −√(1 − u^{2}) + C

= −√(1 − sin^{2 }x) + C

= −√cos^{2 }x + C

= − cos x + C

### Thus, the final integral of sin x is − cos x + C.

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