हिंदी

Find the following integrals: ∫x3+5x2 -4x2dx

Advertisements
Advertisements

प्रश्न

Find the following integrals:

`int (x^3 + 5x^2   -4)/x^2 dx`

योग
Advertisements

उत्तर

Let I = `int (x^3 + 5x^2 - 4)/x^2` dx

`I = int (x + 5 - 4x^(-2))` dx

`I = int x dx + 5 int 1  dx - 4 int x^-2 dx`

`I = x^2/2 + 5x + 4/x + C`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.1 [पृष्ठ २९९]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.1 | Q 11 | पृष्ठ २९९

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find an anti derivative (or integral) of the following function by the method of inspection.

(axe + b)2


Find an antiderivative (or integral) of the following function by the method of inspection.

sin 2x – 4 e3x


Find the following integrals:

`int (4e^(3x) + 1)`


Find the following integrals:

`intsqrtx( 3x^2 + 2x + 3) dx`


Find the following integrals:

`intsec x (sec x + tan x) dx`


Find the following integrals:

`int(sec^2x)/(cosec^2x) dx`


Integrate the function:

`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`


Integrate the function:

`1/(x^2(x^4 + 1)^(3/4))`


Integrate the function: 

`1/(x^(1/2) + x^(1/3))  ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))),  "put x" = t^6]`


Integrate the function:

`(e^(5log x) -  e^(4log x))/(e^(3log x) - e^(2log x))`


Integrate the function:

`cos x/sqrt(4 - sin^2 x)`


Integrate the function:

`e^(3log x) (x^4 + 1)^(-1)`


Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`


Evaluate `int tan^(-1) sqrtx dx`


Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .


The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:


If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is


`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to


`int (dx)/sqrt(9x - 4x^2)` equal


`int (dx)/sqrt(9x - 4x^2)` equals


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


`int sqrt(1 + x^2) dx` is equal to


What is anti derivative of `e^(2x)`


If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.


Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.


What is “an integral of \(f\)” ?


What is integration?


What is \(C\) called in \[\int f(x)\,dx=F(x)+C\]?


For \(n\ne -1\), which is the correct integral of \(x^n\)?


Which antiderivative has derivative \(1\)?


Evaluate \[\int \sec x\tan x\,dx\]


Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?


Evaluate \[\int e^x\,dx\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×