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Evaluate: int(sinx-xcosx)/(x(x+sinx)\ dx...

Evaluate: `int(sinx-xcosx)/(x(x+sinx)\ dx`

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To evaluate the integral \[ I = \int \frac{\sin x - x \cos x}{x(x + \sin x)} \, dx, \] we will follow these steps: ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(sin2x)/(a^2sin^2x+b^2cos^2x)\ dx

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  2. Evaluate: int(tanx)/(a+btan^2x)\ dx

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  3. Evaluate: int(sinx-xcosx)/(x(x+sinx)\ dx

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  4. Evaluate: inttanxtan2xtan3x\ dx

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  5. Evaluate: inttan(x-theta)tan(x+theta)tan2x\ dx

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  6. Evaluate: int{1+2tanx(tanx+secx))^(1/2)dx

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  7. Evaluate: int(sin2x)/(sin(x-pi/3)sin(x+pi/3))\ dx

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  8. Evaluate: (i) int1/(sqrt(1-cos2x))\ dx (ii) int1/(sqrt(1+cosx))\ dx

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  9. Evaluate: (i) intsqrt((1+cos2x)/(1-cos2x))\ dx (ii) intsqrt((1-cosx)/(...

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  10. Evaluate: (i) int(secx)/(sec2x)\ dx (ii) int(cos2x)/((cosx+sinx)^2)\ d...

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  11. Evaluate: (i) int(sin(x-a))/(sin(x-b))\ dx (ii) int(sin(x-alpha))/(sin...

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  12. Evaluate: (i) int(1+tanx)/(1-tanx)\ dx (ii) int(cosx)/(cos(x-a))\ dx

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  13. Evaluate: (i) intsqrt((1-sin2x)/(1+sin2x))\ dx (ii) int(e^(3x))/(e^(3x...

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  14. Evaluate: (i) int(secxtanx)/(3secx+5)\ dx (ii) int(1-cotx)/(1+cotx)\ d...

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  15. Evaluate: (i) int(secx\ cos e c\ x)/(log(tanx)\ dx (ii) int1/(x\ (3+lo...

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  16. Evaluate: (i) int(e^x+1)/(e^x+x)\ dx (ii) int1/(xlogx)\ dx

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  17. Evaluate: (i) int(sin2x)/(acos^2x+bsin^2x)\ dx (ii) int(cosx)/(2+3sinx...

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  18. Evaluate: (i) int(1-sinx)/(x+cosx)\ dx (ii) inta/(b+c e^x)\ dx

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  19. Evaluate: (i) int1/(e^x+1)\ dx (ii) int(cotx)/(logsinx)\ dx

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  20. Evaluate: (i) int(e^(2x))/(e^(2x)-2)\ dx (ii) int(2cosx-3sinx)/(6cosx+...

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