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Integrate the functions(e^x)/((1+e^x)(2+...

Integrate the functions`(e^x)/((1+e^x)(2+e^x)`

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Given `int(e^x)/((1+e^x)(2+e^x)dx`
Let `t=e^x`
`=>dt=e^x dx`
`=>int 1/((1+t)(2+t))dt`..........(1)
...
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NCERT-INTEGRALS-MISCELLANEOUS EXERCISE
  1. Integrate the functions(5x)/((x+1)(x^2+9)

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  2. Integrate the functions1/((x^2+1)(x^2+4)

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  3. Integrate the functions(e^x)/((1+e^x)(2+e^x)

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  4. Integrate the functions1/(sqrt((x+a)(x+b))

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  5. Evaluate the definite integralsint0^1 (dx)/(sqrt(1+x)-sqrt(x))

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  6. Evaluate the definite integralsint(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2...

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  7. Evaluate the definite integralsint0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x...

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  8. Evaluate the definite integralsint0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)...

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  9. Evaluate the definite integrals int(pi/2)^pie^x((1-sinx)/(1-cosx))dx

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  10. Integrate the functions(sqrt(x^2+1)[log(x^2+1)-2logx])/(x^4)

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  11. Integrate the functionstan^(-1)sqrt((1-x)/(1+x))

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  12. Integrate the functions(x^2+x+1)/((x+1)^2(x+2)

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  13. Integrate the functions(2+sin2x)/(1+cos2x)e^x

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  14. Integrate the functionssqrt((1-sqrt(x))/(1+sqrt(x)))

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  15. Evaluate the definite integralsint0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  16. Evaluate the definite integralsint0^(pi/2)sin2xtan^(-1)(sinx)dx

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  17. Choose the correct answersint(cos2x)/((sinx+cosx)^2)dxis equal(A) (-1)...

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  18. Evaluate the definite integralsint0^pi (xtanx)/(secx+tanx)dx

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  19. Evaluate the definite integralsint1^4[|x-1|+|x-2|+|x-3|]dx

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  20. Prove thatint1^3(dx)/(x^2(x+1))=2/3+log2/3

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