Mathematics

# Write a value of $\int { { e }^{ x } } \sec{x} { \left( 1+\tan { x } \right) } dx$

##### SOLUTION
$I=\displaystyle\int{{e}^{x}\sec{x}\left(1+\tan{x}\right)dx}$

$\Rightarrow\,I=\displaystyle\int{{e}^{x}\sec{x}dx}+\displaystyle\int{{e}^{x}\sec{x}\tan{x}dx}$

Consider $\displaystyle\int{{e}^{x}\sec{x}\tan{x}dx}$

Let $u={e}^{x}\Rightarrow\,du={e}^{x}dx$

$dv=\sec{x}\tan{x}dx\Rightarrow\,v=\sec{x}$

$\int u.v dx=u \int vdx-\int \left [\int vdx. \dfrac{du}{dx}.dx \right ]$......by parts formula.

$\Rightarrow\,I=\displaystyle\int{{e}^{x}\sec{x}dx}+{e}^{x}\sec{x}-\displaystyle\int{{e}^{x}\sec{x}dx}+c$

$\therefore\,I={e}^{x}\sec{x}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Medium
Evaluate: $\displaystyle \int \frac{dx}{x^{2}(x^{3}+1)^{\tfrac{2}{3}}}$
• A. $\displaystyle - \left ( 1 - \frac{1}{x^{3}} \right )^{1/3} + c$
• B. $\displaystyle - \left ( 1 - \frac{1}{x^{2}} \right )^{2/3} + c$
• C. $\displaystyle - \left ( 1 + \frac{1}{x^{2}} \right )^{2/3} + c$
• D. $\displaystyle - \left ( 1 + \frac{1}{x^{3}} \right )^{1/3} + c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The quadratic polynomial $p(x)$ has the following properties: $p(x)\ge 0$ for all real number, $p(1)=$ and $p(2)=2$ value of $p(0)+p(3)$ is equal to
• A. $9$
• B. $8$
• C. $None \ of \ these$
• D. $10$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate $\int {({{\sin }^{ - 1}}} x{)^2}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Number of Partial Fractions of $\displaystyle \frac{x^{3}+x^{2}+1}{x^{4}+x^{2}+1}$ is
• A. 3
• B. 4
• C. 7
• D. 2

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Easy
Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020