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If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 ...

If `f^(prime)(x)=3x^2-2/(x^3)` and `f(1)=0` , find `f(x)` .

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RD SHARMA ENGLISH-INDEFINITE INTEGRALS-All Questions
  1. Evaluate: (i) int(2^x+3^x)/(5^x)\ dx (ii) int((a^x+b^x)^2)/(a^x\ b\ ^x...

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  2. Evaluate: (i) int(x^4+x^2+1)\ d(x^2) (ii) intsin(e^x)d(e^x)

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  3. If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

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  4. Evaluate the following: int(3xsqrt(x)+4sqrt(x)+5)\ dx (ii) int(2^x...

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  5. Evaluate: (i) int{sqrt(x)(a x^2+b x+c)}\ dx (ii) int(2-3x)(3+2x)(1-2x...

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  6. Evaluate: (i)int(m/x+x/m+m^x+x^m+m x)\ dx (ii) int(sqrt(x)-1/(sqrt(x))...

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

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

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  9. Evaluate: (i) int(x^(-1//3)+sqrt(x)+2)/(x3)\ dx (ii) int((1+sqrt(x))^2...

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

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

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

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  13. Evaluate: (i) int(sin^3x-cos^3x)/(sin^2xcos^2x)\ dx (ii) int(5cos^3x+6...

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

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  15. Evaluate: int(cos^2x-sin^2x)/(sqrt(1+cos4x))\ dx

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

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

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

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

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

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