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calculus · worked example

Solve ∫ 2x dx = x^2 + C

Method: घात नियम + अचर गुणज. Verified step-by-step solution with our free AI math solver.
Problem

∫2x dx\int 2x \, dx

Step-by-step solution

  1. अचर को बाहर निकालें: ∫2x dx=2∫x dx\int 2x \, dx = 2 \int x \, dx।

  2. घात नियम लागू करें: ∫x dx=x22+C\int x \, dx = \frac{x^2}{2} + C।

  3. गुणा करें: 2⋅x22=x22 \cdot \frac{x^2}{2} = x^2।

  4. अचर जोड़ें: x2+Cx^2 + C।

Answer

x2+Cx^2 + C

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