English

Integrate the following functions w.r.t. x : cosxsin(x-a)

Advertisements
Advertisements

Question

Integrate the following functions w.r.t. x : `cosx/sin(x - a)`

Sum
Advertisements

Solution

Let I = `int cosx/sin(x - a).dx`

= `int cos[(x - a) + a]/sin(x - a).dx`

= `int[cos(x - a)cos a - sin(x - a)sin a)/sin(x - a).dx`

= `int [(cos(x - a)cos a)/sin(x - a) - (sin(x - a)sina)/sin(x - a)].dx`

= `cos a int cot (x - a)dx - sin a int 1 dx`

= cos a log |sin(x – a)| – x sin a + c.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

APPEARS IN

RELATED QUESTIONS

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Evaluate :   `∫1/(cos^4x+sin^4x)dx`


Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 


Integrate the functions:

`e^(tan^(-1)x)/(1+x^2)`


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


Evaluate : `∫1/(3+2sinx+cosx)dx`


Write a value of

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


Write a value of

\[\int e^{2 x^2 + \ln x} \text{ dx}\]

Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


\[\int x \sin^3 x\ dx\]

Integrate the following w.r.t. x : x3 + x2 – x + 1


Integrate the following w.r.t. x:

`2x^3 - 5x + 3/x + 4/x^5`


Evaluate the following integrals:

tan2x dx


Evaluate the following integrals:

`int x/(x + 2).dx`


Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`


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


Integrate the following functions w.r.t. x : sin4x.cos3x


Evaluate the following : `int (1)/(1 + x - x^2).dx`


Evaluate the following:

`int sinx/(sin 3x)  dx`


Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =


Choose the correct options from the given alternatives :

`int (e^x(x - 1))/x^2*dx` =


Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx


If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).


Evaluate the following.

`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx


Evaluate the following.

`int 1/(4"x"^2 - 1)` dx


Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` dx


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx


Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx


Evaluate: `int "x" * "e"^"2x"` dx


`int ("e"^(2x) + "e"^(-2x))/("e"^x)  "d"x`


`int cot^2x  "d"x`


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.


The value of `intsinx/(sinx - cosx)dx` equals ______.


`int sqrt(x^2 - a^2)/x dx` = ______.


`int (logx)^2/x dx` = ______.


Evaluate the following

`int1/(x^2 +4x-5)dx`


Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`


`int "cosec"^4x  dx` = ______.


`int x^2/sqrt(1 - x^6)dx` = ______.


Evaluate the following.

`int "x"^3/sqrt(1 + "x"^4)` dx


Evaluate `int1/(x(x - 1))dx`


`int (x + 1)/(x(1 + xe^x)) dx` is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×