Mathematics

# $\int { (\cfrac { { 2 }^{ x }-5^{ x } }{ 10^{ x } } )dx }$ is equal to __________________.

$\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
$\int { { \left(\displaystyle \frac { 1 }{ a } -\displaystyle \frac { 1 }{ x } \right) }^{ n } } \displaystyle \frac { 1 }{ { x }^{ 2 } } dx$
• A. $\frac { { \left[ \displaystyle \frac { 1 }{ a } +\displaystyle \frac { 1 }{ x } \right] }^{ n+1 } }{ n+1 } +C$
• B. $\frac { { \left[ \displaystyle \frac { 1 }{ a^2 } -\displaystyle \frac { 1 }{ x^2 } \right] }^{ n+1 } }{ n+1 } +C$
• C. None of these
• D. $\frac { { \left[ \displaystyle \frac { 1 }{ a } -\displaystyle \frac { 1 }{ x } \right] }^{ n+1 } }{ n+1 } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the integrals : $\displaystyle \int \dfrac{x^5}{\sqrt{1+x^3}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\smallint \cfrac{{{e^x} - 1}}{{{e^x} + 1}}dx = f\left( x \right) + C$, then f(x) is equal to
• A. $2\log \left| {{e^x} + 1} \right|$
• B. $\log \left| {{e^{2x}} - 1} \right|$
• C. $\log \left| {{e^{2x}} + 1} \right|$
• D. $e^{x}-2\log \left| {{e^x} + 1} \right|$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\displaystyle \int \cfrac{x-1}{\sqrt{x^{2}-1}} \ dx$

$(x^2+1) \log x$