# [SOLVED] integrals

• Feb 12th 2009, 02:46 PM
jahichuanna
[SOLVED] integrals
so we just learned integrals, and i'm having troubles solving this one:

dy/dx = (2e^x + sec(x)tan(x) - x^(1/2))

I've gotten to y= (2e^x)dx + sec(x) - (2/3)x^(3/2), but I can't figure out how to integrate 2e^x. please help?
• Feb 12th 2009, 02:49 PM
Chris L T521
Quote:

Originally Posted by jahichuanna
so we just learned integrals, and i'm having troubles solving this one:

dy/dx = (2e^x + sec(x)tan(x) - x^(1/2))

I've gotten to y= (2e^x)dx + sec(x) - (2/3)x^(3/2), but I can't figure out how to integrate 2e^x. please help?

$\displaystyle \int e^x\,dx=e^x+C$...
• Feb 12th 2009, 02:50 PM
jahichuanna
I get that part, but where did the 2 come from?
• Feb 12th 2009, 02:53 PM
Chris L T521
Quote:

Originally Posted by jahichuanna
I get that part, but where did the 2 come from?

The 2 appears in the original problem.

When you evaluate $\displaystyle \int 2e^x\,dx$, you can rewrite it by applying one of the integral properties. Its equivalent to $\displaystyle 2\int e^x\,dx=2e^x+C$

Does this make sense?
• Feb 12th 2009, 02:55 PM
jahichuanna
ah, ok. thanks.

so the answer is 2e^x + sec x + (2/3)x^(3/2) + c?
• Feb 12th 2009, 02:55 PM
Chris L T521
Quote:

Originally Posted by jahichuanna
ah, ok. thanks.

so the answer is 2e^x + sec x + (2/3)x^(3/2) + c?

(Yes)