Question

Solve ∫ cos(ecx) dx

• A. log cot x
• B. log (cos (ecx) + cot x)
• C. -log (cos (ecx) + cot x)
• D. None of the above

Hint:

For integrals involving trigonometric functions with complex arguments, substitution is often helpful to simplify the expression.

Answer 1

The Correct Option is C

Step 1: Identifying the integral.
The integral ∫ cos(ecx) dx can be solved using substitution and applying standard integration formulas for trigonometric functions.

Step 2: Solving the integral.
By applying the appropriate substitution and applying integration techniques, the solution simplifies to:
∫ cos(ecx) dx = -log (cos(ecx) + cot x) + C

Step 3: Conclusion.
Thus, the correct answer is (C) -log (cos(ecx) + cot x).

Final Answer: -log (cos(ecx) + cot x) + C.