Advertisements
Advertisements
Question
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Advertisements
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(x^3-1)/(x^3+x)dx`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
