Mathematics

# Integrate $\int x{\sec ^2}x dx$

##### SOLUTION

Consider given the given intigration,

Let,

$I=\int{x.{{\sec }^{2}}xdx}$

$\because \int{u.vdx=u\int{vdx-\int{\left( \dfrac{du}{dx}\int{vdx} \right)dx}}}$

$\therefore \int{x.{{\sec }^{2}}xdx}=x\int{{{\sec }^{2}}xdx}-\int{\left( \dfrac{dx}{dx}\int{{{\sec }^{2}}x} \right)}dx$

$=x\tan x-\int{1.\tan x}dx$

$=x\tan x-\log \sec x+C$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate:
$\displaystyle\int\dfrac{a^x}{a^x+1} dx,a>0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int_{-2}^{2} |x \,cos \,\pi x| dx$ is equal to
• A. $\dfrac{4}{\pi}$
• B. $\dfrac{2}{\pi}$
• C. $\dfrac{1}{\pi}$
• D. $\dfrac{8}{\pi}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate with respect to $x$:
$\dfrac {x}{\sqrt {x+2}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Integrate the given function $\cfrac{2x}{({x}^{2}+1)({x}^{2}+3)}$=

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 $\displaystyle f(x)>0 \forall x \in R$