Question

Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of quantity 2 times x to the 5th power plus 6 times x and 5 times x to the 4th power plus 3, dx. Your work must include the use of substitution and the antiderivative.

Answer 1

why, oh why, all those words? Ever hear of actual math notation? If I read it correctly, you want
∫[-1,0] (2x^5 + 6x)^3 * (5x^4 + 3) dx
Note that if we let
u = 2x^5 + 6x
du = (10x^4+6) dx = 2(5x^4+3) dx
That means that we just have
∫[-8,0] 1/2 u^3 du dx = 1/8 u^4 [-8,0] = -512

Answer 2

Why does it all of the sudden go to -8 to 0