Question

Evaluate the integral: e^2x-1/e^x dx

Answer 1

Separate the expression into two terms Pretty easy integral from there.

Answer 2

Like 2^2x/e^x- 1/e^x ?

Answer 3

\[\int\limits_{}^{} \frac{e^{2x}-1}{e^x}~dx=\int\limits_{}^{}\frac{e^{2x}}{e^x}-\frac{1}{e^x}~dx=\int\limits_{}^{}\frac{e^{2x}}{e^x}~dx-\int\limits_{}^{}\frac{1}{e^x}~dx\]

Answer 4

which is\[\int\limits_{ }^{ }e^x~dx~-\int\limits_{}^{ }~e^{-x}~dx\]

Answer 5

\[\int\limits_{}^{}\frac{e^{2x}}{e^x}~dx-\int\limits_{}^{}\frac{1}{e^x}~dx\]
For this part \[\int\limits_{}^{}\frac{e^{2x}}{e^x}~dx\]
it can also be writing as
\[\int\limits_{}^{}\frac{e^{x^2}}{e^x}~dx\]
the e^x cancels out, and you'll get
\[\int\limits_{}^{}e^x~dx\]

Answer 6

for the second part, idku use this method \(\frac{1}{x}=x^{-1}\)
from algebra
\[\int\limits_{}^{}e^x~dx-\int\limits_{}^{}e^{-x}~dx\]

Answer 7

my latex was wrong a lil bit
\(\Large e^{2x}=e^{x+x}=e^{x}*e^{x}=(e^{x})^2\)