At Ask Me Help Desk you can ask questions in any topic and have them answered for free by our experts. To ask questions or participate in answering them you must register for a free account. By registering you will be able to: Get free answers from experts in any of our 300+ topics. Accept money for answers that you provide. Communicate privately with other members (PM). See fewer ads. Sign Up!

Vi Nguyen
May 1, 2009, 09:11 PM
Can anyone help me in finding the antiderivative of:

Sec(x)e^(tan(x))

Antidifferentiation is so confusing!

galactus
May 2, 2009, 05:26 AM
\int sec^{2}(x)e^{tan(x)}dx

Actually, this one is not that bad if you see the sub to make.

Let u=tan(x), \;\ du=sec^{2}(x)dx

Make the subs and it's easy.

Vi Nguyen
May 2, 2009, 10:42 AM
Does this mean this mean that I find the integral of e^(tan(X)), then is the answer e^(tan(x))/tan(x) +C ?

\int sec^{2}(x)e^{tan(x)}dx

Actually, this one is not that bad if you see the sub to make.

Let u=tan(x), \;\ du=sec^{2}(x)dx

Make the subs and it's easy.

galactus
May 2, 2009, 10:49 AM
No, just make the substitution. Have you learned you substitution?.

If we let u=tan(x), \;\ du=sec^{2}(x)dx, it whittles down to

\int e^{\overbrace{u}^{\text{tan(x)}}}\underbrace{du}_{ \text{sec^2(x)dx}}

See why?. The sec^{2}(x)dx is taken care of by the du and the tan(x) is you as

The power in e.

Now, integrate and resub. e^{u} is the easiest to integrate because it stays the same.

Anti-differentiation is not that confusing.Just think of it as the opposite of differentiation.

Once you find the anti-derivative, differentiate and you should get back to the original, e^{tan(x)}sec^{2}(x)

Vi Nguyen
May 2, 2009, 07:00 PM
Thanks your a legend! ;p

No, just make the substitution. Have you learned you substitution?.

If we let u=tan(x), \;\ du=sec^{2}(x)dx, it whittles down to

\int e^{\overbrace{u}^{\text{tan(x)}}}\underbrace{du}_{ \text{sec^2(x)dx}}

See why?. The sec^{2}(x)dx is taken care of by the du and the tan(x) is you as

The power in e.

Now, integrate and resub. e^{u} is the easiest to integrate because it stays the same.

Anti-differentiation is not that confusing.Just think of it as the opposite of differentiation.

Once you find the anti-derivative, differentiate and you should get back to the original, e^{tan(x)}sec^{2}(x)