Thread: [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?

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?

...

I get that part, but where did the 2 come from?

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 , you can rewrite it by applying one of the integral properties. Its equivalent to

Does this make sense?

ah, ok. thanks.

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

Originally Posted by jahichuanna

ah, ok. thanks.

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