Mathematics

# $\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx is

$x+C$

##### SOLUTION
$\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx

$=\displaystyle \int \frac { \sin x+\cos x }{ \sqrt { { (\sin x+\cos x) }^{ 2 } } } dx$

$=\int 1 dx$
$=x+C$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Single Correct Hard
Evaluate: $\int \displaystyle \frac{dx}{x^{3} (x^{3} + 1)^{1/3}}$
• A. $\displaystyle \frac{1}{2} \left ( 1 - \frac{1}{x^{3}} \right )^{1/3} + c$
• B. $\displaystyle \frac{1}{2} \left ( 1 - \frac{1}{x^{3}} \right )^{2/3} + c$
• C. $\displaystyle -\frac{1}{2} \left ( 1 + \frac{1}{x^{3}} \right )^{1/3} + c$
• D. $\displaystyle -\frac{1}{2} \left ( 1 + \frac{1}{x^{3}} \right )^{2/3} + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
Evaluate:$\displaystyle \int_{-1}^{1}\left [ \sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}} \right ]dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve $\displaystyle \int \dfrac {dx}{2x^2-5x+6}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Solve:
$\displaystyle \int \dfrac{1 + x + \sqrt{x + x^2}}{\sqrt{x} + \sqrt{1 + x}}dx$ is equal to
• A. $\dfrac{1}{2} \sqrt{1 + x}C$
• B. $\sqrt{1 + x} + C$
• C. $\dfrac{3}{2} (1 + x)^{32} + C$
• D. $\dfrac{2}{3}(1 + x)^{3/2} + C$

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