English

Find the following integrals: ∫(2x-3cosx+ex)dx

Advertisements
Advertisements

Question

Find the following integrals:

`int(2x - 3cos x + e^x) dx`

Sum
Advertisements

Solution

Let `I = int (2x - 3  cos x + e^x)` dx

`I = 2 int x dx - 3 int cos x dx + int e^x` dx

`I = (2x^2)/2 - 3  sin x + e^x + C`

`I = x^2 - 3  sin x + e^x + C`

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.1 [Page 299]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.1 | Q 16 | Page 299

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

 

Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`

 

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

e2x


Find the following integrals:

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


Find the following integrals:

`intx^2 (1 - 1/x^2)dx`


Find the following integrals:

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


Find the following integrals:

`int (x^3 + 3x + 4)/sqrtx dx`


Find the following integrals:

`int(2x^2 - 3sinx + 5sqrtx) 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^(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:

`cos^3 xe^(log sinx)`


Integrate the function:

`1/sqrt(sin^3 x sin(x + alpha))`


Integrate the function:

`(2+ sin 2x)/(1+ cos 2x) e^x`


Integrate the function:

`tan^(-1) sqrt((1-x)/(1+x))`


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


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


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


`int (xdx)/((x - 1)(x - 2))` equals


`int e^x sec x(1 + tanx) 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 ______.


`int (dx)/sqrt(5x - 6 - x^2)` equals ______.


In \[\int f(x)\,dx\], what is \(f(x)\) called?


What is “an integral of \(f\)” ?


Which statement about indefinite integrals is correct?


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


Evaluate \[\int \sin x\,dx\]


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


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


Evaluate \[\int \frac{dx}{1+x^2}\]


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×