int(4e^(4lnx))/x^5 dx= কত?

Explanation:

Another Explanation (5): সমাধান: আমরা জানি, \(a \ln x = \ln x^a\)। সুতরাং, \(4 \ln x = \ln x^4\) তাহলে, \(4e^{4\ln x} = 4e^{\ln x^4} = 4x^4\) 🎉 এখন, \(\int \frac{4e^{4\ln x}}{x^5} dx = \int \frac{4x^4}{x^5} dx = 4 \int \frac{1}{x} dx\) 🎈 আমরা জানি, \(\int \frac{1}{x} dx = \ln |x| + C\) 🎊 সুতরাং, \(4 \int \frac{1}{x} dx = 4 \ln |x| + C = \ln x^4 + C\) 🎁 অতএব, \(\int \frac{4e^{4\ln x}}{x^5} dx = \ln x^4 + C\)। 💖