Advertisements
Advertisements
Question
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Solution
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)}dx\]
\[ \Rightarrow \int\frac{\left( 1 + x \right)}{x^2 \left( 1 + x \right)}dx + \int\frac{x^2}{x^2 \left( 1 + x \right)}dx\]
\[ \Rightarrow \int\frac{dx}{x^2} + \int\frac{dx}{1 + x}\]
\[ \Rightarrow \int x^{- 2} dx + \int\frac{1}{1 + x}dx\]
\[ \Rightarrow \left[ \frac{x^{- 2 + 1}}{- 2 + 1} \right] + \text{ ln }\left( 1 + x \right) + C\]
\[ \Rightarrow \frac{- 1}{x} + \text{ ln } \left| 1 + x \right| + C\]
APPEARS IN
RELATED QUESTIONS
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
