Mathematics

# Evaluate the following integrals:$\displaystyle \int { \cfrac { a{ x }^{ 2 }+bx+c }{ (x-a)(x-b)(x-c) } } dx$ where $a,b,c$ are distinct.

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int \dfrac{1}{x^2 (x^4 + 1)^{\frac{3}{4}}}dx$ is equal to
• A. $-\dfrac{(1 + x^4)^{\frac{3}{4}}}{x} + C$
• B. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{2x} + C$
• C. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{x^2} + C$
• D. $-\dfrac{(- 1 + x^4)^{\frac{1}{2}}}{x} + C$
• E. $-\dfrac{(1 + x^4)^{\frac{1}{4}}}{x} + C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\int \frac{ln(\frac{x-1}{x+1})}{x^{2}-1}dx$ is equal to

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $x\in \left(0, \dfrac{\pi}{2}\right)$ then $\displaystyle \int{e^{\dfrac{-x}{2}}\dfrac{\sqrt{1-\sin x}}{1+cos x}dx}$=
• A. $-e^{\dfrac{-x}{2}}\sec\dfrac{x}{2}+c$
• B. $e^{\dfrac{x}{2}}\sec\dfrac{x}{2}+c$
• C. $-e^{\dfrac{x}{2}}\sec\dfrac{x}{2}+c$
• D. $e^{-\pi/2}\sec\dfrac{x}{2}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the following: $\dfrac{x-1}{x+1}$

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