Mathematics

# If $g(x)$ is a differentiable function satisfying $\dfrac{d}{dx}{g(x)}=g(x)$ and $g(0)=1,$ then $\int { g\left( x \right) } \left( \dfrac { 2-sin2x }{ 1-cos2x } \right) dx$ is equal to

$g(x)cot$ $x+C$

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

#### Realted Questions

Q1 Subjective Medium
$\text { Evaluate: } \int_{0}^{\pi / 2} \dfrac{\cos ^{2} x}{\cos ^{2} x+4 \sin ^{2} x} d x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Find $\int { \dfrac { 1 }{ 1+tanx } dx }$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of$\displaystyle \int_{1}^{2}\frac{\cos \left ( \log x \right )}{x}dx$  is equal to
• A. $2\sin \left ( \log 2 \right )$
• B. $\displaystyle\sin \log \left ( \frac{1}{2} \right )$
• C. None of these
• D. $\sin \left ( \log 2 \right )$

1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Hard
If $\displaystyle \int x\log \left ( 1+x^{2} \right )dx=\phi \left ( x \right ).\log \left ( 1+x^{2} \right )+\Psi \left ( x \right )+c$ then
• A. $\displaystyle \Psi \left ( x \right )=\frac{1+x^{2}}{2}$
• B. $\displaystyle \phi \left ( x \right )=-\frac{1+x^{2}}{2}$
• C. $\displaystyle \phi \left ( x \right )=\frac{1+x^{2}}{2}$
• D. $\displaystyle \Psi \left ( x \right )=-\frac{1+x^{2}}{2}$

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