English

Evaluate the following integrals: ∫sin4xcos2x.dx - Mathematics and Statistics

Advertisements
Advertisements

Question

Evaluate the following integrals:

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

Sum
Advertisements

Solution

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

= `int(2sin 2x cos 2x)/(cos2x).dx`

= `2int sin 2x .dx`

= `2(-(cos2x)/2) + c`

= – cos 2x + c.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.1 [Page 102]

APPEARS IN

RELATED QUESTIONS

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Integrate the functions:

`(2x)/(1 + x^2)`


Integrate the functions:

`x/(9 - 4x^2)`


Integrate the functions:

`e^(2x+3)`


Integrate the functions:

`x/(e^(x^2))`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


`int (dx)/(sin^2 x cos^2 x)` equals:


\[\int\sqrt{4 x^2 - 5}\text{ dx}\]

Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

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


Write a value of\[\int e^{ax} \sin\ bx\ dx\]


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


Evaluate the following integrals: `int sin 4x cos 3x dx`


Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`


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


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


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

cos8xcotx


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


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


Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`


Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`


Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =


Choose the correct options from the given alternatives :

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


If f'(x) = 4x3 − 3x2  + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Evaluate the following.

`int 1/(sqrt"x" + "x")` dx


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 


`int (sin4x)/(cos 2x) "d"x`


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int x^x (1 + logx)  "d"x`


`int dx/(1 + e^-x)` = ______


`int (cos x)/(1 - sin x) "dx" =` ______.


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


Find `int dx/sqrt(sin^3x cos(x - α))`.


Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.


Evaluate `int(1 + x + x^2/(2!) )dx`


Evaluate the following

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


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


Evaluate the following.

`int x^3 e^(x^2) dx`


Evaluate `int(1 + x + x^2 / (2!))dx`


Evaluate the following.

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


If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Evaluate the following.

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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×