(1 − cos2(7x))2 cos2(7x) sin(7x) dx= (1 − u2)2u2

It seems like you're trying to solve an integral using a trigonometric substitution. Here's how you can do it:

Step 1: Identify the substitution Let u = cos(7x). Then, du = -7sin(7x) dx.

Step 2: Rewrite the integral in terms of u The integral becomes ∫(1 - u^2)^2 * u^2 * du / -7.

Step 3: Simplify the integral This simplifies to -1/7 ∫u^2 * (1 - u^2)^2 du.

Step 4: Expand the integral This expands to -1/7 ∫(u^2 - 2u^4 + u^6) du.

Step 5: Integrate term by term This integrates to -1/7 * [1/3 u^3 - 2/5 u^5 + 1/7 u^7] + C.

Step 6: Substitute u back in terms of x Finally, substitute u = cos(7x) back in to get the final answer: -1/7 * [1/3 cos^3(7x) - 2/5 cos^5(7x) + 1/7 cos^7(7x)] + C.