Find an antiderivative of q(t)=(t+8)^5
1/6(8+t)^6+constant
To find the antiderivative of the given function q(t) = (t + 8)^5, you can apply the power rule of integration. The power rule states that if you have a function of the form f(x) = x^n, where n is any real number except for -1, then the antiderivative is given by F(x) = (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.
Let's apply the power rule to find the antiderivative of q(t) = (t + 8)^5:
Step 1: Identify the exponent. In this case, the exponent is 5.
Step 2: Apply the power rule. The antiderivative of (t + 8)^5 is given by (1/(5+1)) * (t + 8)^(5+1) + C.
Step 3: Simplify the expression. (1/6) * (t + 8)^6 + C is the antiderivative of q(t).
Therefore, the antiderivative of q(t) = (t + 8)^5 is (1/6) * (t + 8)^6 + C, where C is the constant of integration.