Question

S (7x⁶+6x⁵+5x⁴+4x³+6x²+7)dx​

Answer 1

Ответ:

Упростили выражение.

22Sdx⁷+6Sdx³+7Sdx

Пошаговое объяснение:

Первое то,что в скобках (конечно)

1)7x⁶+6x+5x+4x=22Sdx⁷

2)22Sdx⁷+6Sdx³+7Sdx

Answer 2

To integrate the expression S(7x^6 + 6x^5 + 5x^4 + 4x^3 + 6x^2 + 7) dx, you can simply distribute the constant S into each term and then integrate each term separately. The integral of a constant times a function is equal to the constant times the integral of the function. Here's how you can do it step by step:

∫[S(7x^6 + 6x^5 + 5x^4 + 4x^3 + 6x^2 + 7)] dx

= S∫(7x^6 + 6x^5 + 5x^4 + 4x^3 + 6x^2 + 7) dx

Now, integrate each term individually:

∫(7x^6) dx + ∫(6x^5) dx + ∫(5x^4) dx + ∫(4x^3) dx + ∫(6x^2) dx + ∫(7) dx

Let's find the antiderivative of each term:

∫(7x^6) dx = (7/7)x^7 + C1 = x^7 + C1

∫(6x^5) dx = (6/6)x^6 + C2 = x^6 + C2

∫(5x^4) dx = (5/5)x^5 + C3 = x^5 + C3

∫(4x^3) dx = (4/4)x^4 + C4 = x^4 + C4

∫(6x^2) dx = (6/6)x^3 + C5 = x^3 + C5

∫(7) dx = 7x + C6

Now, you can combine all the results:

S∫(7x^6 + 6x^5 + 5x^4 + 4x^3 + 6x^2 + 7) dx = S(x^7 + x^6 + x^5 + x^4 + x^3 + 7x) + C

So, the final result of the integral S(7x^6 + 6x^5 + 5x^4 + 4x^3 + 6x^2 + 7) dx is:

S(x^7 + x^6 + x^5 + x^4 + x^3 + 7x) + C, where C is the constant of integration.