English

Write the Value of ∫ Sec X ( Sec X + Tan X ) D X - Mathematics

Advertisements
Advertisements

Question

Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{  dx }\]

Sum
Advertisements

Solution

\[\int\sec x \left( \sec x + \tan x \right) dx\]
\[ = \int\left( \sec^2 x + \sec x \tan x \right) dx\]
\[ = \tan x + \sec x + C\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 19: Indefinite Integrals - Very Short Answers [Page 198]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 19 Indefinite Integrals
Very Short Answers | Q 52 | Page 198

RELATED QUESTIONS

Integrate the following w.r.t. x `(x^3-3x+1)/sqrt(1-x^2)`


\[\int\frac{x - 1}{\sqrt{x + 4}} dx\]

\[\int\frac{x}{\sqrt{x + 4}} dx\]

Evaluate the following integrals: 

`int "sec x"/"sec 2x" "dx"`

\[\int\frac{\cos 2x}{\left( \cos x + \sin x \right)^2} dx\]

\[\int\frac{1 + \tan x}{1 - \tan x} dx\]

\[\int\frac{e^{2x}}{e^{2x} - 2} dx\]

\[\int\frac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x} dx\]

\[\int\frac{sec x}{\log \left( \text{sec x }+ \text{tan x} \right)} dx\]

Evaluate the following integrals:

\[\int\frac{5x - 2}{1 + 2x + 3 x^2} \text{ dx }\]

\[\int\frac{1}{5 - 4 \cos x} \text{ dx }\]

Evaluate the following integrals:

\[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\]

 


Evaluate the following integrals:

\[\int\frac{\log x}{\left( x + 1 \right)^2}dx\]

 


\[\int\left( x - 3 \right)\sqrt{x^2 + 3x - 18} \text{  dx }\]

Evaluate the following integrals:

\[\int\left( x + 3 \right)\sqrt{3 - 4x - x^2} \text{  dx }\]

Evaluate the following integral :-

\[\int\frac{x}{\left( x^2 + 1 \right)\left( x - 1 \right)}dx\]

Evaluate the following integral:

\[\int\frac{x^2 + 1}{\left( x^2 + 4 \right)\left( x^2 + 25 \right)}dx\]

Evaluate the following integral:

\[\int\frac{3x - 2}{\left( x + 1 \right)^2 \left( x + 3 \right)}dx\]

\[\int\frac{2x + 1}{\left( x + 2 \right) \left( x - 3 \right)^2} dx\]

Evaluate the following integral:

\[\int\frac{1}{x\left( x^3 + 8 \right)}dx\]

 


Evaluate the following integral:

\[\int\frac{2 x^2 + 1}{x^2 \left( x^2 + 4 \right)}dx\]

\[\int\frac{\cos x}{\left( 1 - \sin x \right) \left( 2 - \sin x \right)} dx\]

\[\int\frac{( x^2 + 1) ( x^2 + 4)}{( x^2 + 3) ( x^2 - 5)} dx\]

Evaluate the following integral:

\[\int\frac{1}{\sin^4 x + \sin^2 x \cos^2 x + \cos^4 x}dx\]

Write a value of

\[\int\frac{\left( \log x \right)^n}{x} \text{ dx }\]

Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]


Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]


Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]


Evaluate:

`∫ (1)/(sin^2 x cos^2 x) dx`


Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]


Evaluate the following:

`int sqrt(1 + x^2)/x^4 "d"x`


Evaluate the following:

`int x/(x^4 - 1) "d"x`


Evaluate the following:

`int sqrt(2"a"x - x^2)  "d"x`


Evaluate the following:

`int ("d"x)/(xsqrt(x^4 - 1))`  (Hint: Put x2 = sec θ)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×