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Evalute the following integrals int (d...

Evalute the following integrals
`int (dx)/(1 + e^(x))`

Text Solution

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The correct Answer is:
`" x - log" (1 + e^(x)) + c `
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AAKASH SERIES-INDEFINITE INTEGRALS -EXERCISE - 1.2(VERY SHORT ANSWER QUESTIONS)
  1. Evalute the following integrals int (2x + 3)/(sqrt(x^(2) + 3x - 4)) ...

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

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  3. Evalute the following integrals int (dx)/(1 + e^(x))

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  4. int (1-tanx)/(1+tan x)dx=

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  5. Evaluate the integerals. int (3x^(2) -4)xx dx on R.

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

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  7. Evaluate the following integrals. int(ax^(n-1))/(bx^(n)+c)dx

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  8. Evalute the following integrals int (1)/(x) ("log x")^(2) dx

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  9. Evaluate the integerals. int (sin(log x))/(x)dx on (-1, oo)

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  10. Evaluate the integerals. int (cos (log x))/(x)dx on (0,oo).

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  11. Evaluate the integerals. int (1)/(x log x) dx on (-1, oo)

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  12. Evalute the following integrals int ((1 + log x)^(n))/(x) dx

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  13. Evalute the following integrals int (cot ("log x"))/(x) dx

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  14. Evaluate the integerals. int e ^(x) sin e ^(x) dx on R.

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  15. Evalute the following integrals int e^(x) "cot " e^(x) dx

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  16. Evaluate the integerals. int x ^(3) sin x ^(4) dx on R.

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  17. Evalute the following integrals int 2 x cos " (x^(2) + 1) dx

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  18. Evaluate the integerals. int (e ^(Tan ^(-1)x))/(1+x^(2))dx on I su...

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  19. Evalute the following integrals int 2 xe^(x^(2)) dx

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  20. Evalute the following integrals int " sec (tan x) " sec^(2) x dx

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