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Evaluate int sin(logx)dx....

Evaluate `int sin(logx)dx`.

Text Solution

Verified by Experts

Let `log x =t.` Then,
`x=e^(t)impliesdx=e^(t)dt`
` :. I =int sin(logx)dx`
`=int sin t e^(t) dt`
`=(e^(t))/(2)(sint-cost)+C`
Hence, `int sin(logx)dx=(x)/(2) [sin(logx)-cos(logx)]+C`
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CENGAGE-INDEFINITE INTEGRATION-Question Bank
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  6. intsin4x e^(tan^(2)x)dx = c-A cos^(4)x.e^(tan^(2)x) then A is equal to

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  7. If int dx/(1+sqrt(x+1)+sqrt(x) ) = ax + bsqrtx+c int sqrt((x+1)/x)dx t...

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  8. (4+x^(12))/((x^(6)-2x^(3)+2))dx = x^(alpha)/alpha +x^(beta)/gamma+delt...

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  9. let f(x) =int (4+x^(12))/(x^(4)+x^(3)-7x^(2)-4x+16)dx = A/sqrt3 tan^(-...

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  10. If curve f(x) = int x^(1)(2x^(3)+3x+4)^(3)(1+x+x^(3))dx passes through...

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  11. If f(x) =(3(Inx)^(2)+(In x)^(4))/(x(1+(In x)^(2)-(Inx)^(3))^(2))dx and...

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  12. If (sqrt(e^(7x)))/(root (4)(e^(2x)+e^(-2x)))dx = 1/k(e^(n)+1)^(beta/ga...

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  13. If int(log(ex)e)(log(e^(2)x)e)(log(e^(3)x)e)dx/x = Alog |1+logx|+B log...

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  14. Let int cos^(3)xdx = sin x +(sin^(3)x)/m + (sin^(5)x)/n+c, then n+2m i...

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  15. If (In(ex^(x+1))+(In x^(sqrtx)))^(2)/(1+(x In x)(In e^(2)x^(x)))dx = f...

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  18. Let int (4+3x)/(x^(3)-2x-4)= In|(x-k)/(sqrt(x^(2)+kx+1))|+C, then k^(2...

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  19. If int (x^(8)-12x^(4)+4)/(x^(4)-4x^(2)+2)dx = x^(a)/a + (4x^(b))/b +2x...

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  20. Suppose A = int dx/(x^(2)+6x+25) and B= int dx/(x^(2)-6x-27). If 12(...

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