English

∫x2+x-6(x-2)(x-1) dx = x + ______ + c

Advertisements
Advertisements

Question

`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c

Fill in the Blanks
Advertisements

Solution

`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + 4 log|x-1| + c

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.5: Integration - Q.2

RELATED QUESTIONS

If u and v are two functions of x then prove that

`intuvdx=uintvdx-int[du/dxintvdx]dx`

Hence evaluate, `int xe^xdx`


Integrate the function in x log x.


Integrate the function in x sec2 x.


Integrate the function in `(xe^x)/(1+x)^2`.


`int e^x sec x (1 +   tan x) dx` equals:


Prove that:

`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`


Evaluate the following:

`int sec^3x.dx`


Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.


Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`


If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.


Solve the following differential equation.

(x2 − yx2 ) dy + (y2 + xy2) dx = 0


Evaluate the following.

`int x^2 e^4x`dx


Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx


Choose the correct alternative from the following.

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


Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 


`int 1/(x^2 - "a"^2)  "d"x` = ______ + c


`int "e"^x x/(x + 1)^2  "d"x`


∫ log x · (log x + 2) dx = ?


Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`


The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is


`int(logx)^2dx` equals ______.


`intsqrt(1+x)  dx` = ______


`int1/(x+sqrt(x))  dx` = ______


`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.


The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.


Evaluate:

`int1/(x^2 + 25)dx`


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×