Mathematics

# The value of $\displaystyle\int {\frac{{\sin x + \cos x}}{{\sqrt {1 + \sin 2x} }}} dx$

##### ANSWER

$x + c$

##### SOLUTION
$\displaystyle\int \dfrac{sin x +cos x }{\sqrt{1 + sin(2x)}}dx$
$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{\sqrt{sin^2x+ cos^2x + 2sinxcosx}}dx$
$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{\sqrt{sinx + cosx}^2}dx$
$\displaystyle\rightarrow\int \dfrac{sinx+ cosx}{sinx+ cosx}dx$
$\displaystyle\rightarrow\int dx$
$\displaystyle\rightarrow x + c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Integrate the function    $\cfrac {6x+7}{\sqrt {(x-5)(x-4)}}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
The value of $\displaystyle \int_{-2}^{2} \left | 1-x^{2} \right |dx$ is ......

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate :
$\displaystyle \int_{\tfrac {\pi}{6}}^{\tfrac {\pi}{3}} \dfrac {\sqrt {\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}} dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Evaluate the following integrals:$\displaystyle \int \sqrt{x^{2}+5}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$
Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020