Mathematics

# $\displaystyle\int \dfrac{(x^2+\sin^2x)\sec^2x}{1+x^2}\cdot dx$.

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

#### Realted Questions

Q1 Subjective Hard
$\displaystyle\int e^x\dfrac{(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int _{ 0 }^{ 1 }{ \dfrac { 2\sin ^{ -1 }{ \dfrac { x }{ 2 } } }{ x } } dx$ is equal to
• A. $\displaystyle\int _{ 0 }^{ \pi /6 }{ \cfrac { x }{ \tan { x } } } dx$
• B. $\displaystyle\int _{ 0 }^{ \pi /2 }{ \cfrac { 2x }{ \tan { x } } } dx$
• C. None of these
• D. $\displaystyle\int _{ 0 }^{ \pi /6 }{ \cfrac { 2x }{ \tan { x } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle\int _{ a-n }^{ n }{ { e }^{ x\left( a-x \right) }dx } =\lambda$, then the value of $\displaystyle\int _{ a }^{ n }{ x{ e }^{ x\left( a-x \right) }dx } ,a\neq 2n$, is
• A. $a\lambda$
• B. $2a\lambda$
• C. None of these
• D. $\dfrac{a\lambda}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{1}{\sin x\sqrt{\sin x\cos x}}dx=$
• A. $\sqrt{\tan x}+c$
• B. $-2\sqrt{\tan x}+c$
• C. $2\sqrt{\cot x}+c$
• D. $-2\sqrt{\cot x}+c$

$\int { x{ cos }^{ 2 }2x } dx$