# Integration by substitution ((sin(x))/(1+cos^2(x)))dx

evaluat the indefinite integral ((sin(x))/(1+cos^2(x)))dx

I let

u = 1 + cos^2(x)

then du = -sin^2(x)dx

I rewrite the integral to

- integral sqrt(du)/u

can I set it up like this? should I change u to something else?

I also tried it like this by rewriting the original equation to:

indefinite integral ((sin(x))/(1+cos(x)cos(x)))dx

u = cos(x)

du = -sin(x)dx

then

- integral (du)/(1+(u^2))

Also, can somebody give me directions on how to format equations in this message board to make my questions somewhat clearer.

Thanks alot!

sapiental said:
evaluat the indefinite integral ((sin(x))/(1+cos^2(x)))dx

I let

u = 1 + cos^2(x)

then du = -sin^2(x)dx

I rewrite the integral to

- integral sqrt(du)/u

That's not right. The derivative of $$\cos^2{x}$$ is NOT $$-\sin^2{x}$$.

can I set it up like this?

I also tried it like this by rewriting the original equation to:

indefinite integral ((sin(x))/(1+cos(x)cos(x)))dx

u = cos(x)

du = -sin(x)dx

then

- integral (du)/(1+(u^2))

Yes you can. The final integral is pretty straightforward.

Also, can somebody give me directions on how to format equations in this message board to make my questions somewhat clearer.

neutrino said:
That's not right. The derivative of $$\cos^2{x}$$ is NOT $$-\sin^2{x}$$.

Yes you can. The final integral is pretty straightforward.

neutrino's right - you can't differentiate $$\cos^2{x}$$ as $$-\sin^2{x}$$. If it helps, think of $$\cos^2{x}$$ as $$cos{x} * cos{x}$$. You can then use the chain rule.