Mathematics

Find :$\int { \dfrac { { sec }^{ 2 }x }{ { tan }^{ 2 }x+4 } dx }$

SOLUTION
$\displaystyle\int{\dfrac{{\sec}^{2}{x}dx}{{\tan}^{2}{x}+4}}$
Let $t=\tan{x}\Rightarrow dt={\sec}^{2}{x}dx$
$=\displaystyle\int{\dfrac{dt}{{t}^{2}+4}}$
$=\dfrac{1}{2}{\tan}^{-1}{\dfrac{x}{2}}+c$ using $\displaystyle\int{\dfrac{dx}{{x}^{2}+{a}^{2}}}=\dfrac{1}{a}{\tan}^{-1}{\dfrac{x}{a}}+c$
$\therefore \displaystyle\int{\dfrac{{\sec}^{2}{x}dx}{{\tan}^{2}{x}+4}}=\dfrac{1}{2}{\tan}^{-1}{\dfrac{x}{2}}+c$ where $c$ is the constant of integration.

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 Hard
Prove that $\displaystyle \int_{0}^{\pi} xf(sinx)dx=\dfrac{\pi}{2}\displaystyle \int_{0}^{\pi} f(sinx)dx.$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(\tan x) dx$ is equal to:
• A. $\dfrac{7\pi}{2}$
• B. $\dfrac{7\pi^{2}}{2}$
• C. $\dfrac{3\pi}{2}$
• D. None of these

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\underset{n - 1}{\overset{100}{\sum}} \underset{n - 1}{\overset{n}{\int}} \, e^{x - [x]} dx$ =
• A. $\dfrac{e - 1}{100}$
• B. $100 (e - 1)$
• C. $\dfrac{e^{100} - 1}{100}$
• D. $\dfrac{e^{100} - 1}{e - 1}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve: $\displaystyle \int\limits_0^2 {{x^2}} \cos 2xdx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$

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

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020