int(x+3)/((x+4)^2)e^x\ dx= (e^x)/(x+4)+...

`int(x+3)/((x+4)^2)e^x\ dx=` `(e^x)/(x+4)+C` (b) `(e^x)/(x+3)+C` (c) `1/((x+4)^2)+C` (d) `(e^x)/((x+4)^2)+C`

Text Solution

Verified by Experts

Given,`int(x+3)/((x+4)^2)e^x\ dx`
=`int(x+3-1+1)/((x+4)^2)e^x\ dx`
=`∫e^x[(x+4)/(x+4)^2−1/(x+4)^2]dx`
=`∫e^x[1/(x+4)−1/(x+4)^2]dx`
Now, `∫e^x(f(x)+f′(x))dx=e^xf(x)`
∴`I=e^x/(x+4)`

Topper's Solved these Questions

INCREASING AND DECREASING FUNCTION
RD SHARMA|Exercise Solved Examples And Exercises|232 Videos
INVERSE TRIGONOMETRIC FUNCTION
RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

int x^2 . e^(x^3) dx = (a) e^(x^3) + C (b) e^(x^2) + C (c) 1/3 e^(x^3) + C (d) 1/3 e^(x^2) + C

int(2e^(x))/(3+4e^(x))dx=

int e^(x)((x-2)/((x-1)^(2)))dx is equal to (i) (e^(x))/(x-1)+C (ii) (e^(x))/((x-1)^(2))+C( iii) (2e^(x))/((x-1)^(2))+C( iv )(e^(x)-1)/(x-1)+C

For int (x -1)/( (x +1 ) ^(3)) e ^(x) dx = e ^(x) f (x) + c , f (x) =(x +1) ^(2).

int(2)/((e^(x)+e^(-x))^(2))dx(e^(-x))/(e^(x)+e^(-x))+C(b)-(1)/(e^(x)+e^(-x))+C(c)(-1)/((e^(x)+1)^(2))+C(d)(1)/(e^(x)-e^(-x))+C

int(3e^x+4)/(2e^x-8)dx=

int(e^(x)(1+x))/(cos^(2)(xe^(x)))dx=2(log)_(e)cos(xe^(x))+C(b)sec(xe^(x))+C(c)tan(xe^(x))+C(d)tan(x+e^(x))+C

int((x+2)/(x+4))^(2)+e^(x)dx is equal to e^(x)((x)/(x+4))+c(b)e^(x)((x+2)/(x+4))+ce^(x)((x-2)/(x+4))+c(d)((2xe^(2))/(x+4))+c

int(1)/(x^(2))e^((x-1)/(x))=......," (A) "(x)/(e^(x-1))+c," (B) "e^((x-1)/(x))+c," (C) "-e^((x)/(x-1))+c," (D) "-e^((x-1)/(x))+c

The integral int(1+x-(1)/(x))e^(x+(1)/(x))dx is equal to (1)(x-1)e^(x+(1)/(x))+C(2)xe^(x+(1)/(x))+C(3)(x+1)e^(x+(1)/(x))+C(2)-xe^(x+(1)/(x))+C

RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises

int1/(7+5cosx)\ dx= 1/(sqrt(6))tan^(-1)(1/(sqrt(6))tanx/2)+C (b) 1/(s...
Text Solution
|
int1/(1+cosx+sinx)\ dx= log|1+cotx/2|+C (b) log|1-tanx/2|+C (c) log|...
Text Solution
|
int(x+3)/((x+4)^2)e^x\ dx= (e^x)/(x+4)+C (b) (e^x)/(x+3)+C (c) 1/((x+...
Text Solution
|
int(sinx)/(3+4cos^2x)\ dx log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((...
Text Solution
|
int e^x ((1-sinx)/(1-cosx)) dx= (A) e^xtan(x/2)+C (B) e^xcot(x/...
Text Solution
|
int2/((e^x+e^(-x))^2)\ dx ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x)...
Text Solution
|
int(e^x(1+x))/(cos^2(x e^x))\ dx= 2(log)ecos(x e^x)+C (b) sec(x e^x)+...
Text Solution
|
int(sin^2x)/(cos^4x)\ dx= 1/3tan^2x+C (b) 1/2tan^2x+C (c) 1/3tan^3x+C...
Text Solution
|
The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is...
Text Solution
|
The value of int1/(x+xlogx)\ dx is 1+logx (b) x+logx (c) xlog(1+logx)...
Text Solution
|
intsqrt(x/(1-x))\ dx is equal to sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x...
Text Solution
|
Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C
Text Solution
|
The value of int(sinx+cosx)/(sqrt(1-sin2x))\ dx is equal to sqrt(sin2x...
Text Solution
|
If intxsinx\ dx=-xcosx+alpha, then alpha is equal to sinx+C (b) cosx+C...
Text Solution
|
int(cos2x-1)/(cos2x+1)\ dx= tanx-x+C (b) x+tanx+C (c) x-tanx+C (d) ...
Text Solution
|
int(cos2x-cos2theta)/(cosx-costheta)\ dx is equal to 2\ (sinx+xcosthet...
Text Solution
|
int(x^9dx)/((4x^2+1)^9)i se q u a lto (a)1/(5x)(4+1/(x^2))^(-5)+c ...
Text Solution
|
int(x^3)/(sqrt(1+x^2))\ dx=a(1+x^2)^(3setminus2)+bsqrt(1+x^2)+C , then...
Text Solution
|
int(x^3)/(x+1)\ dx is equal to x+(x^2)/2+(x^3)/3-log|1-x|+C (b) x+(x^...
Text Solution
|
Ifint(dx)/((x+2)(x^2+1))=aln(1+x^2)+btan^(-1)x+1/5ln|x+2|+C Then a=1/...
Text Solution
|