Mathematics

# Evaluate:$\displaystyle \int_{0}^{\dfrac {\pi}{4}}\dfrac {\sin x+\cos x}{9+16\sin 2x}dx$

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

#### Realted Questions

Q1 Subjective Medium
Solve
$\displaystyle \int { \sqrt { { a-x } } } dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int \dfrac{x - 1}{(x - 3) (x - 2) } dx =$
• A. $log (x - 3)^2 - log (x - 2) + c$
• B. $log (x - 3) + log (x - 2) + c$
• C. $log (x - 3)^2 + log (x - 2) + c$\$
• D. $log (x - 3) - log (x - 2) + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int\frac{e^{x}}{(2e^{x}-3)^{2}}dx=$
• A. $\displaystyle \frac{1}{2e^{x}-3}+c$
• B. $\displaystyle \frac{1}{2(2e^{x}-3)^{2}}+c$
• C. $\displaystyle \frac{1}{(2e^{x}-3)^{2}}+c$
• D. $\displaystyle \frac{-1}{2(2e^{x}-3)}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int_{}^{} {\dfrac{{{{\sec }^8}x}}{{\cos ecx}}dx} =$
• A. $\dfrac{{{{\cos }^7}x}}{7} + c$
• B. $\dfrac{7}{{{{\cos }^7}x}} + c$
• C. $\dfrac{1}{{{{\cos }^7}x}} + c$
• D. $\dfrac{1}{{7{{\cos }^7}x}} + c$

Let $\displaystyle 2I_{1}+I_{2}=\int \frac {e^{x}}{e^{2x}+e^{-2x}}dx$  and  $\displaystyle I_{1}+2I_{2}=\int \frac {e^{-x}}{e^{2x}+e^{-2x}}dx$