Integration

[chilly mesa]

for the integration of 1 / (3+sin2x) I got
(root3)/2 root 2 as the coefficient of tan inverse
but in my book the answer says that the coefficient of tan inverse is one by 2 root 2. I think the problem is because of the step of "completing the square"
I considered x to be root3u + 1/root3
but in my book they took 3 common from
the entire eq.
is my ans wrong? if yes why does "not taking out the 3" make my answer wrong?

[waxen sinew]

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[stray bramble]

Yes, you’re meant to take 3 out of the equation. Also, I would recommend to do the u-sub again.

[odd orchid]

here you go

pretty bad mistake

[chilly mesa]

but why?

[chilly mesa]

Im actually new to integration.. can you pls explain why it's wrong?

[stray bramble]

It’s because of how u-subsitution works.

[chilly mesa]

so I can't substitute a variable having a const const term?

[chilly mesa]

like 3x = u

[stray bramble]

You can, you just have to account for the constant that comes after differentiation.

i.e., if you were to let $u=3x$, then $du=3dx$ and thus $\frac13du=dx$.

[fringe moss]

Kocher

[chilly mesa]

ohhhh I get it now. I didn't write the root3 after the differentiation. that way both the root3 will get canceled right? wait a min I'll go and redo this

yes it worked. it was definitely a silly mistake. thank you for pointing it out.

+close

[keen fern]

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