Can anyone help me in finding the antiderivative of:

sec²(x)e^(tan(x))

Antidifferentiation is so confusing!!

\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.

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.

No, just make the substitution. Have you learned u 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 u 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)

Thanks you're a legend! ;p


No, just make the substitution. Have you learned u 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 u 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)