int dx/(x+√x) = ? 

Explanation:

Another Explanation (5): সমাধান: \( \int \frac{dx}{x+\sqrt{x}} \) ধরি, \( x = u^2 \). তাহলে, \( dx = 2u \, du \). তাহলে, ইন্টিগ্রালটি হবে: \( \int \frac{2u \, du}{u^2 + u} = \int \frac{2u \, du}{u(u+1)} = \int \frac{2 \, du}{u+1} \) \( = 2 \int \frac{du}{u+1} \) \( = 2 \ln|u+1| + c \) যেহেতু \( x = u^2 \), তাই \( u = \sqrt{x} \). সুতরাং, \( = 2 \ln|\sqrt{x} + 1| + c \) \( = 2 \ln(\sqrt{x} + 1) + c \) (যেহেতু \( \sqrt{x} + 1 > 0 \)) অতএব, \( \int \frac{dx}{x+\sqrt{x}} = 2 \ln(\sqrt{x} + 1) + c \) 🎉