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Evaluate: (i) int((1+sqrt(x))^2)/(sqrt(x...

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

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

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

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

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

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

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  6. Evaluate: (i) int(1+sinx)/(sqrt(x-cosx))\ dx (ii) int1/(sqrt(1-x^2)(si...

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  7. Evaluate: (i) int(cotx)/(sqrt(sinx)\ )\ dx (ii) int(tanx)/(sqrt(cosx))...

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  8. Evaluate: (i) int(cos^3x)/(sqrt(sinx))\ dx (ii) int(sin^3x)/(sqrt(cosx...

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  9. Evaluate: (i) int1/(sqrt(tan^(-1)x)(1+x^2)\ dx (ii) int(sqrt(tanx))/(s...

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  10. Evaluate: (i) int1/x(logx)^2\ dx (ii) intsin^5xcosx\ dx

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  11. Evaluate (i) inttan^(3//2) xsec^2x\ dx (ii) int(x^3)/((x^2+1)^3)\ dx

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  12. Evaluate: (i) int(4x+2)sqrt(x^2+x+1)\ dx (ii) int(4x+3)/(sqrt(2x^2+3x+...

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  13. Evaluate: (i) int1/(1+sqrt(x))\ dx (ii) inte^cos^(2x)sin2x\ dx

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  14. Evaluate: (i) int(1+cosx)/((x+sinx)^3)\ dx (ii) int(cosx-sinx)/(1+sin2...

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  15. Evaluate: (i) int(sin2x)/((a+bcos2x)^2)\ dx (ii) int(logx^2)/x\ dx

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  16. Evaluate: (i) int(sinx)/((1+cosx)^2)\ dx (ii) intcotxlogsinx\ dx

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  17. Evaluate: (i) intsecxlog(secx+tanx)\ dx (ii) intcos e c\ xlog(cos e c...

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  18. Evaluate: (i) intx^3cosx^4\ dx (ii) intx^3sinx^4\ dx

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  19. Evaluate: (i) int(x^3sin^(-1)x^2)/(sqrt(1-x^4))\ dx (ii) intx^3sin(x^4...

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  20. Evaluate: (i) int((x+1)e^x)/(cos^2(x e^x))\ dx (ii) intx^2\ e^x^3cos(e...

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