How do you integrate $\frac{e^{x}}{\sqrt{1 - e^{2 x}}} d x$ $e^x / sqrt(1-e^(2x)) dx$ ?

Question

How do you integrate $\frac{e^{x}}{\sqrt{1 - e^{2 x}}} d x$ $e^x / sqrt(1-e^(2x)) dx$ ?

1 Answer

Impact of this question

47274 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-20T16:51:19

$arcsin (e^{x}) + C .$ $arcsin(e^x)+C.$

Explanation:

We use Method of Substitution :

Let $e^{x} = t$ $e^x=t$ , so that, $e^{x} d x = d t .$ $e^xdx=dt.$ Also, note that, $e^{2 x} = t^{2} .$ $e^(2x)=t^2.$

Hence, $I = \int \frac{e^{x}}{\sqrt{1 - e^{2 x}}} d x = \int \frac{1}{\sqrt{1 - t^{2}}} d t = arcsin t = arcsin (e^{x}) + C .$ $I=inte^x/sqrt(1-e^(2x))dx=int1/sqrt(1-t^2)dt=arcsint=arcsin(e^x)+C.$

Science

Math

Humanities

... and beyond

How do you integrate $\frac{e^{x}}{\sqrt{1 - e^{2 x}}} d x$ $e^x / sqrt(1-e^(2x)) dx$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate e^x / sqrt(1-e^(2x)) dxex√1−e2xdxe^x / sqrt(1-e^(2x)) dx?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $\frac{e^{x}}{\sqrt{1 - e^{2 x}}} d x$ $e^x / sqrt(1-e^(2x)) dx$ ?