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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 ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  3. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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

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  15. Ifxf(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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  17. The value of int (dx)/((1+sqrtx)(sqrt(x-x^2))) is equal to

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  18. int(2sinx)/(3+sin2x)\ dx

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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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