Mathematics

# If $\int \left( \left (\dfrac{x}{e}\right) ^x +\left(\dfrac{e}{x} \right)^x\right)$ $\ln x .dx= A \left(\dfrac{x}{e} \right)^x + B\left(\dfrac{e}{x}\right) ^x +c$ then $A+ B=$

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
Solve :
$\displaystyle \int { \frac { x+4 }{ { x }^{ 3 }+3{ x }^{ 2 }-10x } dx }$
• A. $\displaystyle \frac { 2 }{ 5 } \ln { \left| x \right| } -\frac { 3 }{ 7 } \ln { \left| x-2 \right| } +\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$
• B. $\displaystyle \frac { 2 }{ 5 } \ln { \left| x \right| } +\frac { 3 }{ 7 } \ln { \left| x-2 \right| } +\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$
• C. $\displaystyle -\frac { 2 }{ 5 } \ln { \left| x \right| } -\frac { 3 }{ 7 } \ln { \left| x-2 \right| } -\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$
• D. $\displaystyle -\frac { 2 }{ 5 } \ln { \left| x \right| } +\frac { 3 }{ 7 } \ln { \left| x-2 \right| } -\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard

$\displaystyle \int_{0}^{\pi/2}\frac{\sin \mathrm{x}\mathrm{d}\mathrm{x}}{(\sin \mathrm{x}+\cos \mathrm{x})^{2}}=$
• A. $\sqrt{2}\log(\sqrt{2}+1)$
• B. $2\log(\sqrt{2}+1)$
• C. $\displaystyle \frac{1}{2\sqrt{2}}log(\sqrt{2}+1)$
• D. $\displaystyle \frac{1}{\sqrt{2}}\log(\sqrt{2}+1)$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle \int\limits_{ - \dfrac{\pi }{2}}^{\dfrac{\pi }{2}} {\dfrac{{\cos x}}{{1 + {e^x}}}} dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int_{0}^{4}\frac{(y^2-4y+5)\sin (y-2)dy}{[2y^2-8y+11]}$ is equal to
• A. 2
• B. -2
• C. none of these
• D.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020