Find the value of the integral $\int _ { 0 } ^ { 1 } \frac { e ^ { x } } { e ^ { x } + 1 } d x$
A) $e + 1$

B) $\ln ( e - 1 )$
C) $\frac { e - 1 } { 2 }$
D) $\ln \frac { e + 1 } { 2 }$
E) $\frac { 1 } { 2 } \ln ( e - 1 )$
F) $\frac { e + 1 } { 2 }$

G) $\frac { 1 } { 2 } \ln ( e + 1 )$

H) $e - 1$

Question

Find the value of the integral $\int _ { 0 } ^ { 1 } \frac { e ^ { x } } { e ^ { x } + 1 } d x$ 
A) $e + 1$ 
 
B) $\ln ( e - 1 )$
C) $\frac { e - 1 } { 2 }$
D) $\ln \frac { e + 1 } { 2 }$ 
E) $\frac { 1 } { 2 } \ln ( e - 1 )$
F) $\frac { e + 1 } { 2 }$ 
 
G) $\frac { 1 } { 2 } \ln ( e + 1 )$

H) $e - 1$

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { 1 } \frac { e ^ { x } } { e ^ { x } + 1 } d x$ can be solved by recognizing it as a standard form that simplifies upon substitution. Let $u = e^x + 1$, then $du = e^x dx$. The limits of integration change accordingly, and the integral simplifies to $\ln |u|$ evaluated from $e^0 + 1$ to $e^1 + 1$, resulting in $\ln \frac { e + 1 } { 2 }$.

Find the Value of the Integral ∫01exex+1dx\int _ { 0 } ^ { 1 } \frac { e ^ { x } } { e ^ { x } + 1 } d x∫01​ex+1ex​dx

Find the Value of the Integral $\int _ { 0 } ^ { 1 } \frac { e ^ { x } } { e ^ { x } + 1 } d x$