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Evaluate: (i) int2xsec^3(x^2+3)tan(x^2+3...

Evaluate: (i) `int2xsec^3(x^2+3)tan(x^2+3)\ dx` (ii) `int((x+1)/x)(x+logx)^2\ dx`

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

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

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  3. Evaluate: (i) int2xsec^3(x^2+3)tan(x^2+3)\ dx (ii) int((x+1)/x)(x+log...

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  4. Evaluate: (i) inttanxsec^2x\ sqrt(1-tan^2x)\ dx (ii) intlogx\ (sin{1+...

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  5. Evaluate: (i) int1/(x^2)cos^2(1/x)\ dx (ii) intsec^4xtanx\ dx

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  6. Evaluate: (i) int(e^(sqrt(x))cos(e^(sqrt(x))))/(sqrt(x))\ dx (ii) int(...

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  7. Evaluate: (i) int(sinsqrt(x))/(sqrt(x))\ dx (ii) int((x+1)e^x)/(sin^2(...

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  8. Evaluate: (i) int5^x+tan^((-1)x)((x^2+2)/(x^2+1))\ dx (ii) int(e^msin^...

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  9. Evaluate: (i) int(cossqrt(x))/(sqrt(x))\ dx (ii) int(sin(tan^(-1)x)/(1...

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  10. Evaluate: (i) int(sin(logx)/x\ dx (ii) int(e^mtan^((-1)x))/(1+x^2)\ dx

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  11. Evaluate: (i) intx/(sqrt(x^2+a^2)+sqrt(x^2-a^2))\ dx (ii) int(xtan^(-1...

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

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

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  14. Evaluate: (i) int(sec^2sqrt(x))/(sqrt(x))\ dx (ii) inttan^3 2xsec2x\ d...

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  15. Evaluate: (i) int(x+sqrt(x+1))/(x+2)\ dx (ii) int5^5^5^x\ \ \ 5^5^x\ \...

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  16. Evaluate: (i) int1/(x\ sqrt(x^4-1))\ dx (ii) intsqrt(e^x-1)\ dx

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  17. Evaluate: (i) int1/((x+1)(x^2+2x+2))\ dx (ii) int(x^5)/(sqrt(1+x^3))\ ...

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  18. Evaluate: (i) int4\ x^3\ sqrt(5-x^2)\ dx (ii) int1/(sqrt(x)+x)\ dx

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  19. Evaluate: (i) int1/(x^2(x^4+1)^(3//4))\ dx (ii) int(sin^5x)/(cos^4x)\ ...

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  20. Evaluate: int(x^2)/(sqrt(x+2))\ dx

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