Mathematics

# Evaluate $\displaystyle \int \frac { \tan x }{( \sec x+ \tan x) } dx$

##### SOLUTION

Solution is:  sec x - tan x + x + C.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Hard
If $f(x) = \dfrac {x + 2}{2x + 3}$, then $\displaystyle \int \left (\dfrac {f(x)}{x^{2}}\right )^{1/2} dx = \dfrac {1}{\sqrt {2}}g \left (\dfrac {1 + \sqrt {2f(x)}}{1 - \sqrt {2f(x)}}\right ) - \sqrt {\dfrac {2}{3}}h \left (\dfrac {\sqrt {3f(x)} + \sqrt {2}}{\sqrt {3f(x)} - \sqrt {2}}\right ) + c$, where
• A. $g(x) = \log |x|, h(x) = \tan^{-1}x$
• B. $g(x) = h(x) = \tan^{-1}x$
• C. $g(x) = \log|x|, h(x) = \log |x|$
• D. $g(x) = \tan^{-1} x, h(x) = \log |x|$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle \int_{-2}^{2}(ax^{3}+bx+c)\ dx$ depends on:
• A. The value of $b$
• B. The value of $a$
• C. The value of $a$ and $b$
• D. The value of $c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following definite integral:

$\displaystyle \int _{0}^1 \dfrac {1-x}{1+x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int(\tan x+\log(\sec x)).e^{x}dx=$
• A. $\log(\sec x)+c$
• B. $\tan x.e^{x}+c$
• C. $-e^{x}\log(\sec x)+c$
• D. $e^{x}$. log(Secx)$+$c

$\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to