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Evaluate the following integral: int1^3(...

Evaluate the following integral: `int_1^3(cos(logx))/x dx`

Text Solution

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Given, `int_1^3(cos(logx))/x dx`
Substituting logx=t
`dt=1/x​dx`
Lim :t=log1=0 to t=log3
`int_0^(log3)(cost)dt`
=sinlog3−0=sinlog3
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^(pi//2)1/(5cos x+3sinx)dx

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Evaluate the following integral: int0^(pi//2)(x+sinx)/(1+cosx)dx

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  15. Evaluate the following integral: int0^(pi//4)(sin x+cosx)/(3+sin2x)dx

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

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  17. Evaluate the following integral: int4^(12)x(x-4)^(1//3)dx

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  18. Evaluate the following integral: int(-1)^1 5x^4sqrt(x^5+1)dx\

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  19. Evaluate the following integral: int0^(pi//4)sin^3 2tcos2t\ dt

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  20. Evaluate the following integral: int0^(pi//2)(cos x)/(1+sin^2x)dx

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