intsqrt((1-x/2))dx=?

Explanation:

Another Explanation (5): সমাধান: ধরি, \( u = 1 - \frac{x}{2} \) তাহলে, \( \frac{du}{dx} = -\frac{1}{2} \) সুতরাং, \( dx = -2 \, du \) এখন, \( \int \sqrt{1 - \frac{x}{2}} \, dx = \int \sqrt{u} \, (-2 \, du) \) \( = -2 \int u^{\frac{1}{2}} \, du \) \( = -2 \cdot \frac{u^{\frac{1}{2} + 1}}{\frac{1}{2} + 1} + c \) \( = -2 \cdot \frac{u^{\frac{3}{2}}}{\frac{3}{2}} + c \) \( = -2 \cdot \frac{2}{3} u^{\frac{3}{2}} + c \) \( = -\frac{4}{3} u^{\frac{3}{2}} + c \) \( = -\frac{4}{3} \left( 1 - \frac{x}{2} \right)^{\frac{3}{2}} + c \) সুতরাং, \( \int \sqrt{1 - \frac{x}{2}} \, dx = -\frac{4}{3} \left( 1 - \frac{x}{2} \right)^{\frac{3}{2}} + c \) 🎉🎉