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If int((x-1)/(x^2))e^x\ dx=f(x)\ e^x+C ,...

If `int((x-1)/(x^2))e^x\ dx=f(x)\ e^x+C ,` then write the value of `f(x)` .

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To solve the problem, we need to evaluate the integral \[ I = \int \frac{x-1}{x^2} e^x \, dx \] and express it in the form \( f(x) e^x + C \), where \( C \) is a constant. Our goal is to find the function \( f(x) \). ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(1-x)\ sqrt(x)\ dx

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  2. Evaluate: int(x+cos6x)/(3x^2+sin6x)\ dx

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  3. If int((x-1)/(x^2))e^x\ dx=f(x)\ e^x+C , then write the value of f(...

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  4. If inte^x\ (tanx+1)secx\ dx=e^x\ f(x)+C , then write the value of f...

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  5. Evaluate: int(2)/(1-cos2x)\ dx

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  6. Write the anti derivative of (3sqrt(x)+1/(sqrt(x))) .

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  7. Evaluate: intcos^(-1)(sinx)\ dx

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  8. Evaluate: int1/(sin^2xcos^2x)\ dx

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  9. intx/(4+x^4)\ dx is equal to 1/4tan^(-1)x^2 (b) 1/4tan^(-1)((x^2)/2) (...

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  10. int1/(cosx+sqrt(3)sinx)\ dx is equal to logtan(pi/3+x/2)+C (b) logtan(...

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  11. intxsecx^2\ dx is equal to 1/2log(secx^2+tanx^2)+C (b) (x^2)/2log(secx...

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  12. If int1/(5+4sinx)\ dx=Atan^(-1)(Btanx/2+4/3)+C , then A=2/3,\ \ B=5/3 ...

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  13. intx^(sinx) ((sinx)/x+cosxdotlogx) dx is equal to (A) x^(sinx)+C (B...

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  14. Integration of 1/(1+((log)e x)^2) with respect to (log)e x is (tan^(-1...

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  15. int(cos8x-1)/(tan2x-cot2x)dx

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  16. If int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C , then a= -1//2 (b...

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  17. int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C ...

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  18. If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal...

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  19. int1/(1+tanx)\ dx=

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  20. int|x|^3\ dx is equal to ( x^4)/4+C (b) (|x|^4)/4+C (c) (x^4)/4+C (d) ...

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