Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Advertisements
उत्तर
`int sqrt(x^2 + 2x + 10) "d"x = int sqrt((x + 1)^2 + 1^2 + 10) "d"x`
= `int sqrt((x + 1)^2 + 9) "d"x`
= `int sqrt((x + 1)^2 + 3^2) "d"x`
Put x + 1 = t
dx = dt
= `int sqrt("t"^2 + 3^2) "dt"`
= `"t"/2 sqrt("t" + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `"t"/2 sqrt("t"^2 + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `((x + 1))/2 sqrt((x + 1)^2 + 3^2) + 3^2/2 log |x + 1 sqrt((x + 1)^2 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x 1 + 9) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 1 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x + 10) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 10)| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
