int tan^3 5x sec^2 5x dx =?  

Explanation:

Another Explanation (5): সমাধান: 🤔 ধরি, \( tan(5x) = u \) তাহলে, \( 5sec^2(5x) dx = du \) সুতরাং, \( sec^2(5x) dx = \frac{1}{5} du \) এখন, \( \int tan^3(5x) sec^2(5x) dx = \int u^3 \frac{1}{5} du \) \( = \frac{1}{5} \int u^3 du \) \( = \frac{1}{5} \cdot \frac{u^4}{4} + C \) \( = \frac{1}{20} u^4 + C \) \( = \frac{1}{20} tan^4(5x) + C \) ✅ অতএব, \( \int tan^3(5x) sec^2(5x) dx = \frac{1}{20} tan^4(5x) + C \) 🥳