COMEDK20269 May 2026Morning ShiftMathematicsIndefinite IntegrationActual
e^ 2x (5x + 3)dx =
Options
- Ae^ 2x 29 [5 (5x+3) - 2 (5x+3)] + C
- Be^ 2x 29 [2 (5x+3) - 5 (5x+3)] + C
- Ce^ 2x 29 [2 (5x+3) + 5 (5x+3)] + C
- De^ 2x 29 [2 (5x+3) + 5 (5x+3)] + C
Correct answer
C. e^ 2x 29 [2 (5x+3) + 5 (5x+3)] + C
Step-by-step solution
Using the standard integral formula: e^ ax (bx + c)dx = e^ ax a^2 + b^2 [a (bx + c) + b (bx + c)] + C Comparing the given integral e^ 2x (5x + 3)dx with the standard form, we get a = 2 , b = 5 , and c = 3 . Substituting these values into the formula: e^ 2x (5x + 3)dx = e^ 2x 2^2 + 5^2 [2 (5x + 3) + 5 (5x + 3)] + C = e^ 2x 29 [2 (5x + 3) + 5 (5x + 3)] + C Answer: e^ 2x 29 [2 (5x+3) + 5 (5x+3)] + C