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Evaluate the following integrals: int...

Evaluate the following integrals: `int_0^1(24x^3)/((1+x^2)^4)dx`

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Given:
`int_0^1(24x^3)/((1+x^2)^4)dx`
`I=int_0^1(24x^3)/((1+x^2)^4)dx`
Let `1+x^2 = t implies 2xdx=dt`
When `x = 0, t = 1 + 0^2 =1`
When `x = 1, t = 1 + 12 = 2`
So, the new limits are`1`and `2`
Then
...
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
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  2. Evaluate the following integrals: int0^((pi)^(2//3))sqrt(x)cos^2x^(...

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  3. Evaluate the following integrals: int0^1(24x^3)/((1+x^2)^4)dx

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  6. If In=int0^(pi//4)tan^n x dx , show that 1/(I2+I4),1/(I3+I5),1/(I4+...

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  7. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

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  8. Evaluate: int0^1x(tan^(-1)x)^2dx

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  10. Evaluate: int0^1xsqrt((1-x^2)/(1+x^2))dx

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  11. Evaluate the following integrals: int0^a(sin)^(-1)sqrt(x/(a+x))dx

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  12. Evaluate the following integrals: int1^2 1/(x(1+logx)^2)dx

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  13. Evaluate the following integrals: int0^(pi//4)(sin^2xcos^2x)/((sin...

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  14. Evaluate the following integrals: int0^(pi//2)(tanx)/(1+m^2tan^2x)d...

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  15. Evaluate: int0^1|5x-3|dx

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  16. Evaluate: (i) \int(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=...

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  17. int (1/e)^e |logx|dx =

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  18. If a >0, find int0^(3a)|x^2-a^2|dxdot

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  19. If [dot] denotes the greatest integer function, then find the valu...

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  20. Evaluate: int0^3[x]dx

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