Question

Rewrite the integration in terms of u. ∫ x cos(8x²) dx = cos(u) + C

Answer 1

To rewrite the given integral in terms of u, we can use the substitution method. Let u = 8x². Then, we have du = 16x dx. Rearranging the equation, we have dx = du / (16x). Substituting these values into the integral, we get: ∫ x cos(8x²) dx = ∫ (u/16) cos(u) du. Taking out the constant factor, the integral becomes: (1/16) ∫ u cos(u) du. Integrating this new integral will result in cos(u) + C, where C is the constant of integration. Therefore, the rewritten integral in terms of u is cos(u) + C.

Step-by-step explanation:

To rewrite the given integral in terms of u, we can use the substitution method. Let u = 8x². Then, we have du = 16x dx. Rearranging the equation, we have dx = du / (16x). Substituting these values into the integral, we get:

∫ x cos(8x²) dx = ∫ (u/16) cos(u) du. Taking out the constant factor, the integral becomes:

= (1/16) ∫ u cos(u) du.

Integrating this new integral will result in cos(u) + C, where C is the constant of integration. Therefore, the rewritten integral in terms of u is cos(u) + C.