intdx/(3-4x)^(2/3)=  কোনটি ?

Explanation:

Another Explanation (5): প্রশ্ন: ∫ dx/(3-4x)^(2/3) = ? সমাধান: ধরি, u = 3 - 4x তাহলে, du = -4 dx সুতরাং, dx = -du/4 এখন, ∫ dx/(3-4x)^(2/3) = ∫ (-du/4)/u^(2/3) = -1/4 ∫ u^(-2/3) du = -1/4 * (u^(-2/3 + 1))/(-2/3 + 1) + C [যেখানে C একটি ধ্রুবক] = -1/4 * (u^(1/3))/(1/3) + C = -3/4 * u^(1/3) + C u এর মান বসিয়ে পাই, = -3/4 * (3-4x)^(1/3) + C অতএব, ∫ dx/(3-4x)^(2/3) = -3/4(3-4x)^(1/3) + C 🥳 সুতরাং, উত্তর: -3/4(3-4x)^(1/3) 🤩