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Evaluate the following integral: int1^2(...

Evaluate the following integral: `int_1^2(3x)/(9x^2-1)dx`

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Given, I=`int_1^2(3x)/(9x^2-1)dx`
Let`9x^2-1=t`
so,`18xdx=dt`
when x=1 then t=8
when x=2 then t=35
I=`1/6 int _8^(35)dt/t`
=`1/6 (log35-log8)`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int2^4x/(x^2+1)dx

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

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  3. Evaluate the following integral: int1^2(3x)/(9x^2-1)dx

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  4. Evaluate the following integral: int0^a x/(sqrt(a^2+x^2))dx

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  5. Evaluate the following integral: int0^1x e^x^2dx

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  6. Evaluate the following integral: int0^1(2x)/(1+x^4)dx

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

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  8. Evaluate the following integral: int0^(pi//2)1/(5cos x+3sinx)dx

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  9. Evaluate the following integral: int0^1(e^x)/(1+e^(2x))dx

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  10. Evaluate the following integral: int1^3(cos(logx))/x dx

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  11. Evaluate the following integral: int0^asqrt(a^2-x^2)dx

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  12. Evaluate the following integral: int0^(pi//2)sqrt(sinvarphi)cos^5varph...

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  13. Evaluate the following integral: int0^(pi//2)(sintheta)/(sqrt(1+costhe...

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  14. Evaluate the following integral: int0^1(sqrt(tan^(-1)x))/(1+x^2)dx

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  15. Evaluate the following integral: int0^1tan^(-1)\ ((2x)/(1-x^2))dx

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  16. Evaluate the following integral: int0^(pi//2)(dx)/(acosx+bsinx)x

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  17. Evaluate the following integral: int0^pi(sinx)/(sinx+cosx)dx

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  18. Evaluate the following integral: int0^1tan^(-1)x\ dx

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  19. Evaluate the following integral: int0^(pi//4)(sqrt(t a n x)+sqrt(cotx)...

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  20. Evaluate the following integral: int0^pi1/(5+3cosx)dx

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