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Find int (3x-5)/(x (x^(2)+2x+4))dx....

Find `int (3x-5)/(x (x^(2)+2x+4))dx.`

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The correct Answer is:
`- (5)/(4) log |x| + (5)/(8) log |x^(2)+ 2x + 4| + (17)/(4 sqrt(3)) tan^(-1) ((x + 1)/(sqrt(3)) ) + c `
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AAKASH SERIES-INDEFINITE INTEGRALS -EXERCISE - 1.3(SHORT ANSWER QUESTIONS )
  1. Evalute the following integrals int (3x - 2)/((x - 1)(x +2)(x-3))dx

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  2. Evalute the following integrals int (1)/((x -a)(x -b)(x-c))dx

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  3. int (1)/((x^(2)+a^(2))(x^(2)+b^(2)))dx=

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  4. Evaluate the integerals. int (x^(2))/((x+1) (x+2)^(2))dx

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  5. Evalute the following integrals int (7x -4)/((x -1)^(2)(x+2)) dx

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  6. Evalute the following integrals int (2x^(2) + x + 1)/((x+3)(x-2)^(2)...

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  7. Evalute the following integrals int (x+ 3)/((x-1)(x^(2)+1)) dx

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  8. Evalute the following integrals int (1)/((1 -x)(x^(2)+4)) dx

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  9. Evalute the following integrals int (2x + 3)/((x + 3)(x^(2)+ 4)) dx

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  10. Evalute the following integrals int (1)/((x+ 1)^(2)(x^(2) + 1)) dx

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  11. Find int (2x^(2) -5x +1)/(x^(2)(x^(2) -1))dx.

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  12. Find int (3x-5)/(x (x^(2)+2x+4))dx.

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  13. Evaluate the following integral int (2x + 1)/(x(x^(2) + 4)^(2)) dx

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  14. Evaluate the integerals. int (dx )/(e ^(x) +e^(2x))

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  15. Evalute the following integrals int (1)/(e^(x)-1)dx

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  16. Evalute the following integrals int (e^(x))/(2e^(2x) + 3e^(x)-2) dx

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  17. Evaluate the integerals. int (sin x cos x)/(cos ^(2)x +3 cos x+2)d...

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  18. Evalute the following integrals int (cos x)/(sin^(2) x + 4 sin x + 5...

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  19. Evalute the following integrals int sqrt(e^(x) - 4) dx on [ log(e)^(...

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  20. Evalute the following integrals int sqrt(1 + sec x ) dx on ((2n - (...

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