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Evaluate: int(x+cos6x)/(3x^2+sin6x)\ dx...

Evaluate: `int(x+cos6x)/(3x^2+sin6x)\ dx`

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`=int(x+cos6x)/(3x^2+sin6x)\ dx`

Let, `3x^2+sin6x=t`

`(6x+6cos6x)dx=dt`

`=(1)/(6)int(6x+6cos6x)/(3x^2+sin6x)\ dx`

`=(1)/(6)int(dt)/(t)\ `

`=(1)/(6)log t+C\ `

`=(1)/(6)log (3x^2+sin6x)+C\ `

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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
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  2. Evaluate: int(1-x)\ sqrt(x)\ dx

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  12. intxsecx^2\ dx is equal to 1/2log(secx^2+tanx^2)+C (b) (x^2)/2log(secx...

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  13. If int1/(5+4sinx)\ dx=Atan^(-1)(Btanx/2+4/3)+C , then A=2/3,\ \ B=5/3 ...

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  15. Integration of 1/(1+((log)e x)^2) with respect to (log)e x is (tan^(-1...

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  18. int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C ...

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  19. If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal...

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  20. int1/(1+tanx)\ dx=

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