Are the formulas correct?

[Tueseve728]

Integral sec^2(5x-1)dx=(1/5)tan(5x-1)+C (To see if correct differntiate)

and...

integral xe^xdx=xe^x-e^x+C

Thanks so much for your help!

 

[soroban]

Hello, Tueseve728!

They gave you the answers . . . and asked you the check them.
. . They even told you how to check them.

So what exactly is your problem?

\(\displaystyle \int\sec^2(5x\,-\,1)\,dx\:=\:\frac{1}{5}\tan(5x\,-\,1)\,+\,C\)
(To see if correct, differntiate)

Well, do it!

The derivative of \(\displaystyle \frac{1}{5}\tan(5x\,-\,1)\,+\,C\;\) is: \(\displaystyle \:\frac{1}{5}\cdot\sec^2(5x\,-\,1)\cdot 5\,+\,0\)

Is that equal to the original function in the integral?
. . If it is, the answer is correct.

 

[Tueseve728]

hey i need help with the dx for integral xe^x dx=xe^x-e^x+C are these equal? I dont know how to do the derivative. thanks so much!