Mathematics

# Integrate $\displaystyle\int \dfrac{x^3-1}{x^2}$

##### SOLUTION
$\int { \cfrac { { x }^{ 3 }-1 }{ { x }^{ 2 } } } =\int { x-{ x }^{ -2 } }$
$=\int { x } -\int { { x }^{ -2 } }$
$=\cfrac { { x }^{ 2 } }{ 2 } -\cfrac { x-1 }{ -1 }$
$=\cfrac { { x }^{ 2 } }{ 2 } +\cfrac { 1 }{ x }$

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

#### Realted Questions

Q1 Single Correct Hard
Evaluate the given integral.
$\displaystyle\int { \cfrac { \cos { 2x } -1 }{ \cos { 2x } +1 } } dx$
• A. $\tan { x } -x+C$
• B. $x+\tan { x } +C$
• C. $-x-\cot { x } +C$
• D. $x-\tan { x } +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium

lf $\displaystyle \int_{0}^{\pi/{2}}\log(\sin \mathrm{x})\mathrm{d}\mathrm{x}=\mathrm{k}$ then $\displaystyle \int_{0}^{\pi/{2}}\log(\cos x)d{x}$
• A. $\dfrac{k}{2}$
• B. $2k$
• C. $-3k$
• D. $k$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard

$\displaystyle \int_{0}^{\pi /4}x\tan^{4}xdx=$
• A. $\dfrac{2}{3}\ln2+\dfrac{\pi^{2}}{32}-\dfrac{\pi}{12}-\dfrac{1}{6}$
• B. $\dfrac{2}{3}\ln2-\dfrac{\pi^{2}}{32}+\dfrac{\pi}{12}+\dfrac{1}{6}$
• C. $\dfrac{2}{3}\ln2+\dfrac{\pi^{2}}{32}-\dfrac{\pi}{12}-+\dfrac{1}{6}$
• D. $\dfrac{2}{3}\ln2+\dfrac{\pi^{2}}{32}-\dfrac{\pi}{6}-\dfrac{1}{6}$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Let $T=\int_0^{\ln2}\dfrac{2e^{3x}+ 3e^{2x}-6e^x}{6(e^{3x}+e^{2x}-e^x+1)}dx,$ then $e^T=\frac{p}{q}$ where p and q are coprime to each other, then the value of $p+ q$ is

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int { (\cfrac { { 2 }^{ x }-5^{ x } }{ 10^{ x } } )dx }$ is equal to __________________.
• A. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• B. $\cfrac { { 2 }^{ x } }{ \log _{ e }{ 2 } } +\cfrac { 5^{ x } }{ \log _{ e }{ 5 } } +c$
• C. $\cfrac { { 5 }^{ -x } }{ \log _{ e }{ 5 } } -\cfrac { 2^{ -x } }{ \log _{ e }{ 2 } } +c$
• D. $\cfrac { { 2 }^{ -x } }{ \log _{ e }{ 2 } } -\cfrac { 5^{ -x } }{ \log _{ e }{ 5 } } +c$