Finding the Anti-Derivative of (sin x)^3/2 - Tips and Tricks

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SUMMARY

The discussion focuses on finding the anti-derivative of the function \( \int \sin^{3/2} x \, dx \). A key insight shared is the transformation of the expression, where \( \sin^{3/2} x \) can be rewritten as \( (\sin^3 x)^{1/2} \). This simplification aids in applying integration techniques effectively. Participants emphasize the importance of recognizing algebraic identities in calculus to facilitate the integration process.

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  • Knowledge of algebraic manipulation techniques.
  • Experience with integration techniques, including substitution and integration by parts.
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[SOLVED] Antiderivative of (sin x)^3/2

How do I find the anti-derivative of:

\int sin^{3/2}x

I can't see where to start...

Thanks
 
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LadiesMan said:
How do I find the anti-derivative of:

\int sin^{3/2}x dx

I can't see where to start...

Thanks

sin^{\frac{3}{2}}x=(sin^3x)^\frac{1}{2}

Remember that

(ab)^n=a^nb^n
 
ahhh ok thank you
 

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