MHT CET202613 April 2026Morning ShiftMathematicsIndefinite IntegrationActual
30x¹⁴ + 15^x 225 x¹⁵ + 15^x , dx =
Options
- Ax¹⁵ + 15x¹⁴ + 30x¹³ + c , where c is the constant of integration
- B(x¹⁵ + 15^x) 2 + c , where c is the constant of integration
- C(x¹⁵ + 15^x)^2 + c , where c is the constant of integration
- D(x¹⁵ + 15^x) + c , where c is the constant of integration
Correct answer
C. (x¹⁵ + 15^x)^2 + c , where c is the constant of integration
Step-by-step solution
Let I = 30x¹⁴ + 15^x 225 x¹⁵ + 15^x , dx Let x¹⁵ + 15^x = t Differentiating both sides with respect to x , we get (15x¹⁴ + 15^x 15) , dx = dt Multiplying by 2 , we get (30x¹⁴ + 2 15^x 15) , dx = 2 , dt Since 2 15 = (15^2) = 225 , this becomes (30x¹⁴ + 15^x 225) , dx = 2 , dt Substituting this into the integral, we obtain I = 2 t , dt I = 2 t + c I = (t^2) + c I = (x¹⁵ + 15^x)^2 + c Answer: (x¹⁵ + 15^x)^2 + c , where c is the constant of integration