Mathematics

# $\int \dfrac{x - 1}{(x - 3) (x - 2) } dx =$

$log (x - 3) - log (x - 2) + c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Find $\begin{pmatrix}\int ^{\pi /4}_0 \dfrac{dx}{\cos^3 x\sqrt{2\sin2x}}\end{pmatrix}$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$I = \int \sqrt {\dfrac {a - n}{n - b}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value(s) of $\int _{ 0 }^{ 1 }{ \cfrac { { x }^{ 4 }{ \left( 1-x \right) }^{ 4 } }{ 1+{ x }^{ 2 } } } dx$ is (are)
• A. $\cfrac{2}{105}$
• B. $0$
• C. $\cfrac{71}{15}-\cfrac{3\pi}{2}$
• D. $\cfrac{22}{7}-\pi$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Solve $\displaystyle\int\limits_1^3 {\frac{{\log x}}{{{{\left( {x + 1} \right)}^2}}}dx}$
• A. $I=\dfrac{3\log 3}{4}+\log \left( 2 \right)$
• B. $I=\dfrac{\log 3}{4}-\log \left( 2 \right)$
• C. None of these
• D. $I=\dfrac{3\log 3}{4}-\log \left( 2 \right)$

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 $\displaystyle f(x)>0 \forall x \in R$