Mathematics

# Solve $\int{\sec{x}dx}=$

##### SOLUTION
$\int \sec x dx = \int \dfrac{\sec x (\sec x + \tan x)}{\sec x + \tan x} dx$

$= \log | \sec x + \tan x| + c$
(or)
$= \log |\tan (\dfrac{\pi}{4} + \dfrac{x}{2})| + c$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate : $\displaystyle\int^1_0\dfrac{dx}{\sqrt{5x+3}}$
• A. $\dfrac{2}{5}(\sqrt{8}+\sqrt{3})$
• B. $\dfrac{2}{5}\sqrt{8}$
• C. None of these
• D. $\dfrac{2}{5}(\sqrt{8}-\sqrt{3})$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int \frac{1}{\left ( x+1 \right )\sqrt{x^{2}+x+1}}dx$
• A. $\displaystyle =-\log \left | \frac{1}{x+1}-\frac{1}{2}+\frac{\sqrt{x^{2}+x+1}}{x-1} \right |$
• B. $\displaystyle =-\log \left | \frac{1}{x-1}-\frac{1}{2}+\frac{\sqrt{x^{2}+x-1}}{x-1} \right |+C$
• C. $\displaystyle =-\log \left | \frac{1}{x-1}-\frac{1}{2}+\frac{\sqrt{x^{2}+x+1}}{x+1} \right |+C$
• D. $\displaystyle =-\log \left | \frac{1}{x+1}-\frac{1}{2}+\frac{\sqrt{x^{2}+x+1}}{x+1} \right |+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Passage Medium
Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$

On the basis of above information, answer the following questions:

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle \int_{0}^{4} \dfrac{(y^2-4y+5)(sin(y-2)dy}{(2y^2-8y+1)}$ is
• A. $2$
• B. $-2$
• C. None of these
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate: $\displaystyle \int_{0}^{\pi /4}\tan^{5}xdx$
• A. $\displaystyle \log 2-\frac{1}{4}$
• B. $0$
• C. $\displaystyle \log 2+\frac{1}{4}$
• D. $\displaystyle \frac{1}{2}\log 2-\frac{1}{4}$