Mathematics

# Write a value of $\displaystyle\int { \cfrac { \sin { x } }{ \cos ^{ 3 }{ x } } } dx$

##### SOLUTION
$I=\displaystyle\int{\dfrac{\sin{x}}{{\cos}^{3}{x}}dx}$

$=\displaystyle\int{\tan{x}{\sec}^{2}{x}dx}$

Let $t=\sec{x}\Rightarrow\,dt=\sec{x}\tan{x}dx$

$=\displaystyle\int{t\,dt}$

$=\dfrac{{t}^{2}}{2}+c$

$=\dfrac{{\sec}^{2}{x}}{2}+c$     ........where $t=\sec{x}$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
$\displaystyle\int x\cos^3x\sin x dx$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Solve $\displaystyle \int_0^{\pi/2} \dfrac{x\,\,\sin\,x \,cos\,x}{cos^4x+\sin^4x}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle\int^e_1e^x\left(\dfrac{1+x log x}{x}\right)dx$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle 4\int \frac{a^{6}+x^{8}}{x}dx$ is equal to
• A. $\displaystyle I=\sqrt{a^{6}+x^{8}}+\frac{a^{3}}{2}\ln\left | \frac{\sqrt{a^{6}+x^{8}}+a^{3}}{\sqrt{a^{6}+x^{8}}-a^{3}}\right |+c$
• B. $\displaystyle a^{6}\ln \frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}+c$
• C. $\displaystyle a^{6}\ln \frac{\sqrt{a^{6}+x^{8}}+a^{3}}{\sqrt{a^{6}+x^{8}}-a^{3}}+c$
• D. $\displaystyle I=\sqrt{a^{6}+x^{8}}+\frac{a^{3}}{2}\ln\left | \frac{\sqrt{a^{6}+x^{8}}-a^{3}}{\sqrt{a^{6}+x^{8}}+a^{3}}\right |+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Easy
Evaluate:
$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020