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

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

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To evaluate the integral \( I = \int \frac{(x^4 - x)^{1/4}}{x^5} \, dx \), we can follow these steps: ### Step 1: Simplify the Integral First, we rewrite the integral in a more manageable form: \[ I = \int \frac{(x^4 - x)^{1/4}}{x^5} \, dx = \int \frac{(x^4(1 - \frac{1}{x^3}))^{1/4}}{x^5} \, dx \] This can be simplified further by factoring out \( x^4 \): ...
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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(2)^(2)^(2)^x\ \ 2^2^x\ \ 2^x\ dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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