Mathematics

# Evaluate the following integral:$\displaystyle \int { \cfrac { 1 }{ \left( \sin { x } -2\cos { x } \right) \left( 2\sin { x } +\cos { x } \right) } } dx$

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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 Hard
$I=\displaystyle \int { \dfrac { e^{ x } }{ (e^{ x }+1)^{ \frac { 1 }{ 4 } } } } dx$ is equal to
• A. $\dfrac { e^{ 2x }-e^{ -2x } }{ 2 } \quad +\quad c$
• B. `$\dfrac { e^{ 2x }+e^{ -2x } }{ 2 } \quad +\quad c$
• C. $\frac { e^{ x }\quad -e^{ 2x } }{ 2 } \quad +\quad c$
• D. none of these

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Integrate:
$\int_{0}^{\frac{\pi }{2}}{\dfrac{\sin x}{\sin x+\cos x}}dx$ Then
• A. $I=\dfrac{\pi }{3}$
• B. $I=\dfrac{\pi }{6}$
• C. $I=\dfrac{\pi }{5}$
• D. $I=\dfrac{\pi }{4}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate:- $\int {\dfrac{1}{{3{x^2} + 5x + 7}}dx.}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate the given integral.
$\int { { e }^{ 2x } } \left( -\sin { x } +2\cos { x } \right) dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
Obtain: $\int _{ a }^{ b }{ \sin { x } } dx$ as limit of sum.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020