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int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) i...

`int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x)` is equal to (a) `-e^(tan^(-1)x)+c` (b) `e^(tan^(-1)x)+c` (c) `-xe^(tan^(-1)x)+c` (d) `xe^(tan^(-1)x)+c`

A

` - e^(tan^(-1)x)+c`

B

` e^(tan^(-1)x)+c`

C

`-x e^(tan^(-1)x)+c`

D

`x e^(tan^(-1)x)+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int e^(tan^(-1)x) (1+x+x^(2))(-((1)/(1+x^(2)))dx)`
`= -int e^(tan^(-1)x)(1+(x)/(1+x^(2)))dx`
`= -int e^(tan^(-1)x)dx-int x(e^(tan^(-1)x))/(1+x^(2))dx`
`= -int e^(tan^(-1)x)dx-x e^(tan^(-1)x)+int e^(tan^(-1)x) dx+C`
`= -x e^(tan^(-1)x)+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  2. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  3. Find the value of " int x sec^(2)x dx

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  4. int x sinx sec^(3)x dx is equal to

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  5. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  6. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

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  7. int e^(x^4) (x^3) dx is equal to

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  8. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

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  9. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

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  10. int((x+2)/(x+4))^2 e^xdx is equal to

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  11. inte^(tanx)(secx-sinx)dxi se q u a lto e^(tanx)cosx+C e^(tanx)sinx...

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  12. int(cos e c^2x-2005)/(cos^(2005)x)dx is equal to (a) -(cotx)/((cosx)^...

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  13. int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx is equal to (a) -x e^(x^(2)...

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  14. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  15. If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x)...

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  16. The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-...

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  17. int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

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  18. int(2sinx)/(3+sin2x)dx is equal to

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  19. 4int(sqrt(a^6+x^8))/x dx is equal to (a)sqrt(a^6+x^8)+(a^3)/2ln|...

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  20. IfI(m , n)=intcos^m xsinn xdx ,t h e n7I(4,3)-4I(3,2)i se q u a lto c...

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