Question

Find the indefinite integral of 13sec(x)tan(x)dx. Use a computer algebra system to confirm your result. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

The integral of 13sec(x)tan(x)dx is 13sec(x) + C, where C is the constant of integration. This follows from the fact that the derivative of sec(x) is sec(x)tan(x) and integration reverses differentiation.

Step-by-step explanation:

To find the indefinite integral of 13sec(x)tan(x)dx, we can recognize that the derivative of sec(x) is sec(x)tan(x). Thus, integrating sec(x)tan(x) will give us sec(x). Since we have a constant multiple of 13, the integral becomes:

∫ 13sec(x)tan(x)dx = 13 ∫ sec(x)tan(x)dx

This simplifies to:

13sec(x) + C

where C is the constant of integration. To confirm our result, a computer algebra system can be used.