Mathematics

# $\int \, sin \, x \, cos x \, cos 2x \, cos 4x \, cos 8x \, dx$ =

$\dfrac{sin 16 x}{256} + c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
Evaluate the given integral.
$\displaystyle\int{\dfrac{\sqrt{1+\cos{2x}}}{2}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $f(a+b-x)=f(x)$ then $\int _{a}^{b}{x\ f(x)dx}=$

• A. $\int _{ a }^{ b }{ f\left( x \right) dx }$
• B. $(a+b)\int _{ a }^{ b }{ f\left( x \right) dx }$
• C. $0$
• D. $\left( \dfrac { a+b }{ 2 } \right) \int _{ a }^{ b }{ f\left( x \right) dx }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle I_1=\int_{ -100 }^{101}\frac{ \:dx}{(5+2x-2x^2)(1+e^{(2-4x)} )}$and $\displaystyle I_2=\int_{ -100 }^{101}\frac{ \:dx}{(5+2x-2x^2)}$ then
$\dfrac{I_1}{I_2}$ is
• A. $2$
• B. $1$
• C. $-\displaystyle \frac{1}{2}$
• D. $\displaystyle \frac{1}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Solve $\displaystyle\int\limits_1^3 {\frac{{\log x}}{{{{\left( {x + 1} \right)}^2}}}dx}$
• A. $I=\dfrac{3\log 3}{4}+\log \left( 2 \right)$
• B. $I=\dfrac{\log 3}{4}-\log \left( 2 \right)$
• C. None of these
• D. $I=\dfrac{3\log 3}{4}-\log \left( 2 \right)$

$\displaystyle\int \dfrac{1}{n\sqrt{n^3-1}}dx$.