MHT CET202520 Apr 2025Evening ShiftMathematicsIndefinite IntegrationActual
e^ ⁻¹ 2 x 1+4 x^2 =
Options
- A4 e ^ ⁻¹ 2 x + c , where c is the constant of integration
- Be^ ⁻¹ 2 x +c, where c is the constant of integration
- Ce^ ⁻¹ 2 x 2 +c, where c is the constant of integration
- D2 e ^ ⁻¹ 2 x + c , where c is the constant of integration
Correct answer
C. e^ ⁻¹ 2 x 2 +c, where c is the constant of integration
Step-by-step solution
The integral e^ ⁻¹ 2x 1+4x^2 dx is evaluated using substitution. Let u = ⁻¹ 2x . The derivative is du dx = 2 1+4x^2 , so 1 1+4x^2 dx = 1 2 du . Substituting gives e^u 1 2 du = 1 2 e^u du = 1 2 e^u + C . Replacing u yields the final result: 1 2 e^ ⁻¹ 2x + C . This corresponds to option C .