Mathematics

# Solve:$\displaystyle \int \dfrac { \sin ^ { 3 } x + \cos ^ { 3 } x } { \sin ^ { 2 } x \cos ^ { 2 } x } d x$

##### SOLUTION
$\int \dfrac{(sin^{3}+cos^{3}x)}{sin^{2}x\cos^{2}x}dx$

$= \int (\dfrac{sin x}{\cos^{2}x}+\dfrac{\cos x}{\sin^{2}x})dx = \int (\sec x\tan x+cosec\,xcotx)dx$

$= sec x-cosec x+c$

$= \dfrac{1}{\cos x}-\dfrac{1}{\sin x}+c$

$= \dfrac{\sin x-\cos x}{\sin x\,\cos x}+c$

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

#### Realted Questions

Q1 Subjective Hard
Solve : $\displaystyle \int_{0}^{2}{x\sqrt{x+2}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle sin(ax)sin(bx)=cos(ax)cos(bx)(a,b\neq 0$ & $a\neq b)$, then $\displaystyle \int \frac {sin(ax)+cos(bx)}{cos(ax)+sin(bx)}dx$ is
• A. $\displaystyle \frac {1}{a}ln |secax|+C$
• B. $\displaystyle \frac {1}{b}ln |sinbx|+C$
• C. $\displaystyle \frac {1}{a}ln |cosecbx|+C$
• D. $\displaystyle \frac {1}{b}ln |cosax|+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Matrix Hard

 If $\displaystyle \int \frac {dx}{x^{1/3}+2}=$$g(x)+C$ where $g(0)=12ln2$, then $[g(-1)]$ is equal to$($ where $[.]$ denotes greatest integer function$)$ $1$ If $\displaystyle \int (sec x)^{9/5}(cosec x)^{1/5}dx=k tan^{m}x+C$,then $km$ is equal to $3$ Let $\displaystyle \int \frac {dx}{cot^{2}x-1}=\frac {1}{l}\ln \left | sec2x+tan2x \right|-\frac {x}{m}+C$,then $\iota + m$ is equal to $6$ Let $\displaystyle \int \frac{\left ( 1+\frac{1}{x} \right )dx}{\sqrt{1+xe^{x}}}=\ln \left | \frac {g(x)-1}{g(x)+1} \right |+C$, then $[g^{2}(1)]$ is equal to$($where $[.]$ denotes greatest integer function$)$ $7$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Solve $\displaystyle\int\dfrac {\sqrt{\tan x}}{\sin x \cos x}dx$
• A. $I=3\sqrt{\tan x}+C$
• B. $I=\sqrt{\tan x}+C$
• C. $None\ of\ these$
• D. $I=2\sqrt{\tan x}+C$

$\displaystyle\int x^n\log_ex\ dx$