Mathematics

# $\int { \cfrac { \cos { x } -1 }{ \sin { x } +1 } } { e }^{ x }dx$ is equal to:

$\cfrac { { e }^{ x }\cos { x } }{ 1+\sin { x } } +c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Hard
A tank initially holds 10 lit. of fresh water. At t = 0, a brine solution containing $\displaystyle \frac{1}{2}$ kg of salt per lit. is poured into tank at a rate 1 lit/min while the well-stirred mixture leaves the tank at the same rate. Find the concentration of salt in the tank at any time $t$.
• A. $- 5e^{-t} - 5$ kg/L
• B. $5e^{t} + 5$ kg/L
• C. none of the above
• D. $- 5e^{-t} + 5$ kg/L

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
$\int { \dfrac { x }{ \left( x-1 \right) \left( x-2 \right) } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate$\int\limits_{} {\dfrac{{\cos x}}{{\left( {2 + \sin x} \right)\left( {3 + 4\sin x} \right)}}dx.}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $f(x)$ and $g(x)$ be two function satisfying $f(x^2)+g (4-x)=4x^3, g(4-x)+g(x)=0$, then the value of $\int_{-4}^{4} f(x^2)dx$ is:
• A. 64
• B. 256
• C.
• D. 512

Prove that $\displaystyle\int_0^{\pi/2}$ $ln(\sin x)dx=\displaystyle\int_0^{\pi/2}ln(cos x)dx=\int_0^{\pi/2}\,\,ln(sin2x)dx=-\dfrac{\pi}{2}.ln 2$.