Solved by AI teacher · Physics

∫ (sin³m + cos³m) / (sin²m cos²m) dm

Concept: Trigonometric integral simplification

Question

\int \csc^2 x dx = -\cot x + C

Try it yourself first

Hint: Pehle fraction ko alag-alag karke dekho, jaise

\frac{A+B}{C} = \frac{A}{C} + \frac{B}{C}

1
Separate terms
Split fraction • Numerator sum
$\frac{A+B}{C} = \frac{A}{C} + \frac{B}{C}$
2
Simplify first term
sin³m / (sin²m cos²m) • sin m / cos²m • tan m sec m
$\frac{\sin m}{\cos^2 m} = \tan m \sec m$
3
Simplify second term
cos³m / (sin²m cos²m) • cos m / sin²m • cot m cosec m
$\frac{\cos m}{\sin^2 m} = \cot m \csc m$
4
Integrate terms
∫ tan m sec m dm = sec m • ∫ cot m cosec m dm = -cosec m
$\int (\sec m \tan m + \csc m \cot m) dm$

-cot m + tan m + C

Remember: Trigonometric integrals ko simplify karne ke liye identities use karo.

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\int \frac{\sin^3 x + \cos^3 x}{\sin^2 x \cos^2 x} dx

ko solve karne ke liye, pehla step kya hona chahiye?

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