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

Evaluate: (i) `int((1+logx)^2)/x\ dx` (ii) `int(sec^2(2tan^(-1)x))/(1+x^2)\ dx`

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Let's solve the given integrals step by step. ### (i) Evaluate the integral: \[ \int \frac{(1 + \log x)^2}{x} \, dx \] **Step 1: Substitution** ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: (i) int(4\ (sin^(-1)x)^3)/(sqrt(1-x^2))\ dx (ii) int(log(tan...

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  2. Evaluate: (i) int(sinx)/(sqrt(3+2cosx))\ dx

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  3. Evaluate: (i) int((1+logx)^2)/x\ dx (ii) int(sec^2(2tan^(-1)x))/(1+x^2...

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  4. Evaluate: (i) int(tanxsec^2x)/((a+btan^2x)^2)\ dx (ii) intsec^3xtanx\ ...

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  5. Evaluate: (i) intx^3sinx^4\ dx (ii) inte^(-x)\ cos e c^2(2\ e^(-x)+5)\...

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  6. Evaluate: (i) intsqrt(tanx)(1+tan^2x)\ dx (ii) int{f\ (a x+b)}^nf^...

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  7. Evaluate: int(sin2x)/((a+bcosx)^2)

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  8. Evaluate: int(2)^(2)^(2)^x\ \ 2^2^x\ \ 2^x\ dx

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  9. Evaluate: int1/(sqrt(sin^3xsin(x+alpha)))\ dx ,\ alpha!=npi,\ \ n in ...

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  10. Evaluate: int((x^4-x)^(1//4))/(x^5)\ dx

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  11. Evaluate: int(sec^4x)/(sqrt(tanx))\ dx

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  12. Evaluate: int(cos^9x)/(sinx)\ dx

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  13. Evaluate: int1/(root(4)((x-1)^3 (x+2)^5)\ dx .

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  14. Evaluate: (i) intx^x(1+logx)\ dx (ii) intx^(2x)\ (1+logx)\ dx

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  15. Evaluate: intx/(x-sqrt(x^2-1))dx

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  16. Evaluate: int(cos^3x)/(sin^2x+sinx)dx

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  17. Evaluate: (i) int(logx)/x\ dx (ii) int(log(1+1/x))/(x(1+x))\ dx

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  18. Evaluate: (i) int((1+sqrt(x))^2)/(sqrt(x))\ dx (ii) intsqrt(1+e^x)\ e^...

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  19. Evaluate: (i) intcos^2x3sinx\ dx (ii) int(e^x)/((1+e^x)^2)\ dx

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  20. Evaluate: (i) intcot^3x\ cos e c^2x\ dx (ii) int({e^msin^(-1)x})/(sqrt...

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