Mathematics

# Integrate :  $\dfrac{\cos \, x}{(1 - \sin \, x) (2 - \sin \, x)}$

##### SOLUTION
$\int \dfrac{\cos x}{(1-\sin x)(2-\sin x)}dx$

substitute $u=1-\sin x\rightarrow du=-\cos x dx$

$\int -\dfrac{1}{u(u+1)}dx$

$-\left ( \int \dfrac{1}{u}-\dfrac{1}{u+1}du\right )$

$-(\ln u-\ln (u+1))$

$-\ln|1-\sin x|+\ln |2-\sin x|+C$

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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
If $\displaystyle f\left ( x \right )=\int\frac{1}{x-\sqrt{x^{2}+1}}$ and $\displaystyle f\left ( 0 \right )=\frac{1+\sqrt{2}}{2}$, then $f(1)$ is equal to
• A. $\displaystyle \frac {-1}{\sqrt {2}}$
• B. $\displaystyle 1+ \sqrt{2}$
• C. $\displaystyle \dfrac12\log \left ( 1+\sqrt{2} \right )$
• D. $\displaystyle \log \left (\sqrt{ \sqrt{2}-1} \right )$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Integrate :  $dx-dy+ydx+xdy=0$.
• A. $x^2-y^2+2xy=C$.
• B. $x^3-y^3+3xy=C$.
• C. $x^4-y^4+4xy=C$.
• D. $x-y+xy=C$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Multiple Correct Hard
$\displaystyle\int{\frac{dx}{(x+1)(x-2)}}=A\log{(x+1)}+B\log{(x-2)}+C$, where
• A. $AB=0$
• B. none of these
• C. $A+B=0$
• D. $\displaystyle\frac{A}{B}=-1$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { \cfrac { 1 }{ \sqrt { 1+4{ x }^{ 2 } } } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
Simplify: $\displaystyle \int \frac{\left ( x^{4}-x \right )^{1/4}}{x^{5}}dx$
• A. $\displaystyle \frac{2}{5}\left ( 1-\frac{1}{x^{3}} \right )^{-5/4}+c$
• B. $\displaystyle \frac{4}{15}\left ( 1-\frac{1}{x^{3}} \right )^{-5/4}+c$
• C. $\displaystyle \frac{2}{5}\left ( 1-\frac{1}{x^{3}} \right )^{5/4}+c$
• D. $\displaystyle \frac{4}{15}\left ( 1-\frac{1}{x^{3}} \right )^{5/4}+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020