Question

Evaluate the integral by making the given substitution. sec2 1 x6 x7 dx, u = 1 x6

Answer 1

To evaluate the integral, we can substitute u = 1/x^6. This allows us to rewrite the integral in terms of u as ∫(-u^2) du/u. Integrating this expression gives us the final result of - (1/(2x^12)) + C.

Step-by-step explanation:

To evaluate the integral, we make the given substitution, u = 1/x^6. Differentiating u with respect to x gives du/dx = -6/x^7. Rewriting the integral in terms of u, we have ∫(sec^2(x)/x^6) dx = ∫(-u^2) du/u = - ∫u du = - (u^2/2) + C = - (1/(2x^12)) + C.