Integral

[KEYWEST17]

Evaluate the Integral: 2/(T+7)^4 dt

So far I set u=T+7
du/dx= 1 dx <<< From where 'x' is coming ?? You need to pay attention to your work!Integral of 2 u^-4 du

2u-5/(-5) <<< NO

\(\displaystyle \int u^n du \ = \ \frac{u^{n+1}}{n+1} \ + \ C\)

In your case:

n = -4

n + 1 = -4 + 1 = -3

not sure where to go from there

 

[KEYWEST17]

So my final answer should be 2(T+7)^4/-3

 

[lookagain]

So my final answer should be 2(T+7)^4/-3

You must use lower case for each letter representing the same variable.

Let''s stick to the lower case.

You were indicated to use these (by another user):

u = t + 7 . . . . . (adjusting to lower case)
n = -4
n + 1 = -3

The integral (using the formula shown to you by another user here) equals

[2(t + 7)^(-3)]/(-3) + C . . . . . You cannot leave off this arbitrary constant C, see?


\(\displaystyle = \frac{2(t + 7)^{-3}}{-3} + \bigg{C}\)

\(\displaystyle = \frac{-2}{3(t + 7)^{3}} + \bigg{C}\)