intsqrt(2x+3)dx এর মান কত?

Explanation:

Another Explanation (5): সমাধান: 🤔 ধরি, \(2x+3 = u\) তাহলে, \(2dx = du\) ⟹ \(dx = \frac{du}{2}\) এখন, \(\int \sqrt{2x+3} dx = \int \sqrt{u} \frac{du}{2}\) \( = \frac{1}{2} \int u^{\frac{1}{2}} du\) \( = \frac{1}{2} \cdot \frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1} + c\) 🥳 \( = \frac{1}{2} \cdot \frac{u^{\frac{3}{2}}}{\frac{3}{2}} + c\) \( = \frac{1}{2} \cdot \frac{2}{3} u^{\frac{3}{2}} + c\) \( = \frac{1}{3} u^{\frac{3}{2}} + c\) \( = \frac{1}{3} (2x+3)^{\frac{3}{2}} + c\) 🤩 সুতরাং, \(\int \sqrt{2x+3} dx = \frac{1}{3} (2x+3)^{\frac{3}{2}} + c\) 💖