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Evaluate: (i) int(x^e+e^x+e^e)\ dx (i...

Evaluate:
(i) `int(x^e+e^x+e^e)\ dx`
(ii) `intsqrt(x)(x^3-2/x)\ dx`

Text Solution

Verified by Experts

(i) `int(x^e+e^x+e^e)\ dx`

`=(x^(e+1))/(e+1)+e^x+e^e x+C`

(ii) `intsqrt(x)(x^3-2/x)\ dx`

`=intx^(7/2)dx-int2x^(-1/2)dx`

`=(2x^(9/2))/(9)-4sqrt(x)+C`
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(m/x+x/m+m^x+x^m+m x)\ dx (ii) int(sqrt(x)-1/(sqrt(x)))^2...

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  2. Evaluate: (i) int((1+x)^3)/(sqrt(x))\ dx (ii) int{x^2+e^(logx)+(e/2...

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  3. Evaluate: (i) int(x^e+e^x+e^e)\ dx (ii) intsqrt(x)(x^3-2/x)\ dx

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  4. Evaluate: (i) int1/(sqrt(x))(1+1/x)\ dx (ii) int(x^6+1)/(x^2+1)\ dx

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  5. Evaluate: (i) int(x^(-1//3)+sqrt(x)+2)/(x^3)\ dx (ii) int((1+sqrt(x)...

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  6. Evaluate: (i) intsqrt(x)(3-5x)\ dx (ii) int((x+1)(x-2))/(sqrt(x))\ d...

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  7. Evaluate: (i) int(x^5+x^(-2)+2)/(x^2)\ dx (ii) int(5\ x^4+12\ x^3+7...

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  8. Evaluate: (i) int(sin^2x)/(1+cosx)\ dx (ii) int(sec^2x+cos e c^2x)\...

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  9. Evaluate: (i) int(sin^3x-cos^3x)/(sin^2xcos^2x)\ dx (ii) int(5cos^3...

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  10. Evaluate: (i) int(tanx+cotx)^2\ dx (ii) int(1-cos2x)/(1+cos2x)\ dx

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  11. Evaluate: (i) int(cosx)/(1-cosx)\ dx (ii) int(cos^2x-sin^2x)/(sqrt...

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  12. Evaluate: (i) int1/(1-cosx)\ dx (ii) int1/(1-sinx)\ dx

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  13. Evaluate: (i) int(tanx)/(secx+tanx)\ dx (ii) int(cos e c\ x)/(cos e c\...

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  14. Evaluate: (i) int1/(1+cos2x)\ dx (ii) int1/(1-cos2x)\ dx

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  15. Evaluate: (i) inttan^(-1)((sin2x)/(1+cos2x))\ dx (ii) intcos^(-1)(si...

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  16. Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2...

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  17. Evaluate: (i) int((x^3+8)(x-1))/(x^2-2x+4)\ dx (ii) int(atanx+bcotx)...

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  18. Evaluate: (i) int(x^3-3x^2+5x-7+x^2\ a^x)/(2x^2)\ dx (ii) int(cosx)...

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  19. Evaluate: (i) int(1-cosx)/(1+cosx)\ dx (ii) int{3sinx-4cosx+5/(cos^...

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  20. If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

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