Integrate
-$\int e ^ { x } \sec ^ { 2 } \left( e ^ { x } \right) d x$
A) $\frac { \tan \left( \mathrm { e } ^ { x } \right) } { \mathrm { e } ^ { \mathrm { x } } }$ + C
B) tan( $e ^ { x }$ ) + C
C) $\tan ^ { 2 }$ ( $e ^ { x }$ ) + C
D) $e ^ { x }$ tan( $e ^ { x }$ ) + C
E) none of these

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = e^x $, then $ du = e^x dx $. The integral becomes $\int \sec^2(u) du = \tan(u) + C = \tan(e^x) + C$.

Integrate - ∫exsec⁡2(ex)dx\int e ^ { x } \sec ^ { 2 } \left( e ^ { x } \right) d x∫exsec2(ex)dx

Integrate
- $\int e ^ { x } \sec ^ { 2 } \left( e ^ { x } \right) d x$