Question

Evaluate the integral ∫7tan⁵(x)dx. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

To evaluate the integral ∠7tan⁵(x)dx, we need to use trigonometric identities and substitution, followed by the inclusion of the constant of integration C.

Step-by-step explanation:

The question requires evaluating the integral ∠7tan⁵(x)dx. To approach this integration, we use the identity ∠tan²(x)dx = ∠²(5)dx, and recognize that a reduction strategy involving trigonometric identities and substitution is needed. The integral can be simplified by recognizing tan(x) as sin(x)/cos(x) and using trigonometric identities to express the integral in a more straightforward form. We can then apply substitution to reduce the integral to a more familiar form. After integration, we should not forget to include the constant of integration, represented by C. The correct use of substitution and trigonometric identities is crucial in arriving at the final answer for the integral.