Is the Antiderivative of 1/x Actually ln(x)?

[chemical]

ive been trying to do this problem and its annoying!


The function to be integrated: 1 + 1/x + x dx


Interval: [8,2]

when anti differentiating the fuction i get x + x^2/2 + lnx but i don't think the integral of 1/x is lnx...help would be appreciated

 

[cookiemonster]

1
The function to be integrated: 1 + - + x dx
x

What does this mean? + - +?

cookiemonster

 

[chemical]

sorry updated on error

 

[cookiemonster]

You can separate the problem into three little ones.

$$\int_2^8 \left( 1 + \frac{1}{x} + x \right) \,dx = \int_2^8 1 \, dx + \int_2^8 \frac{1}{x} \, dx + \int_2^8 x \, dx$$

And

$$\int \frac{dx}{x} = \ln{|x|}$$

cookiemonster

 

[chemical]

thanks a lot cookie. kudos goes out to you