What is the integral of (sqrt(16-e^{2x)})/(e^x) ?

The integral of (sqrt(16-e^{2x)})/(e^x) is -(sqrt(16-e^{2x)})/(e^x)-arcsin(1/4 e^x)+C

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integral of (sqrt(16-e^{2x)})/(e^x)

\int \frac{16 - e ^{2 x}}{e ^{x}} d x

- \frac{16 - e ^{2 x}}{e ^{x}} - arcsin (\frac{1}{4} e^{x}) + C

Solution steps

\int \frac{16 - e ^{2 x}}{e ^{x}} d x

Apply Integration By Parts

= - \frac{16 - e ^{2 x}}{e ^{x}} - \int \frac{e ^{x}}{16 - e ^{2 x}} d x

\int \frac{e ^{x}}{16 - e ^{2 x}} d x = arcsin (\frac{1}{4} e^{x})

= - \frac{16 - e ^{2 x}}{e ^{x}} - arcsin (\frac{1}{4} e^{x})

Add a constant to the solution

= - \frac{16 - e ^{2 x}}{e ^{x}} - arcsin (\frac{1}{4} e^{x}) + C

What is the integral of (sqrt(16-e^{2x)})/(e^x) ?
The integral of (sqrt(16-e^{2x)})/(e^x) is -(sqrt(16-e^{2x)})/(e^x)-arcsin(1/4 e^x)+C