ind the following indefinite integral:∫((−6𝑥−3)𝑥5)d𝑥

Sure, let's solve the indefinite integral step by step.

Given integral is ∫((−6x−3)x^5)dx

Step 1: Distribute x^5 into the terms inside the parentheses.

= ∫(-6x^6 - 3x^5)dx

Step 2: Now, we can separate this into two integrals.

= ∫-6x^6 dx - ∫3x^5 dx

Step 3: Now, we can pull constants out of the integral.

= -6∫x^6 dx - 3∫x^5 dx

Step 4: Now, we can integrate each term. The integral of x^n with respect to x is (1/(n+1))x^(n+1).

= -6 * (1/7)x^7 - 3 * (1/6)x^6 + C

Step 5: Simplify the expression.

= -(6/7)x^7 - (1/2)x^6 + C

So, the indefinite integral of ((−6x−3)x^5)dx is -(6/7)x^7 - (1/2)x^6 + C.