Indefinate Integral

Integrate separately.

\(\displaystyle \int e^{x}dx-\frac{7}{8}\int xdx\)

It is very basic and routine.
 
The integral of e^e is e^e and cant be simplified further.

-7/8 integral of xdx is -7/8 .

The final answer should be 7/8 e^x ?
 
CatchThis2 said:
The integral of e^e is e^e and cant be simplified further.

-7/8 integral of xdx is -7/8 .

The final answer should be 7/8 e^x ?
Click to expand...

The integration of e^x is e^x + C " Notify if proof is needed ".

The integration of xdx is (x^2)/2 + C.

Therefore, the integration of the above is : (-7/16)(x^2) .
 
The program I am inserting that into won't accept that answer. I do see how you got x^2 over 2 but I don't see how -7/16 works?

I tried (-7/8)(x^2) but that doesn't work either.
 
The integral of e^e would be \(\displaystyle x{e^{e}}\).

e^e is a constant.

Thus, \(\displaystyle \int(e^{x}-\frac{7x}{8})dx=\int e^{x}dx-\frac{7}{8}\int xdx=e^{x}-\frac{7}{16}x^{2}+C\)

The 7/16 comes from adding 1 to the exponent and then dividing that into 7/8.

(7/8)/2=7/16
 
Then I do not want to tell you. That is the correct solution for the given integral.

Try it with and without the C. The C is just a constant of integration.
 
Could the problem be:

\(\displaystyle \int \frac{e^x - 7x}{8} dx \ = \ \frac{2e^x - 7x^2}{16} \ + \ C\)
 
So your problem statement should have been:

CatchThis2 said:
Any idea how to evaluate?

[(e^x)-(7x)]/8
Click to expand...

Note those grouping [ ... ] brackets.

After 62 posts, you ought to have learnt the importance of those grouping symbols and proper way to use those utilizing PEMDAS!!!
 
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