Find the integrals of the following: 1×2+4x+2

Find the integrals of the following:

`1/sqrt(xx^2 + 4x + 2)`

Sum

`int ("d"x)/sqrt(x^2 + 4x + 2) = int ("d"x)/sqrt((x + 2)^2 - 2^2 + 2)`

= `int ("d"x)/sqrt((x + 2)^2 - 4 + 2)`

= `int ("d"x)/sqrt((x + 2)^2 - 2)`

= `int ("d"x)/sqrt((x + 2)^2 - (sqrt(2))^2`

Put x + 2 = t

dx = dt

= `int ("d"x)/sqrt("t"^2 - (sqrt(2))^2`

`int ("d"x)/sqrt(x^2 - "a"^2) = log|x + sqrt(x^2 - "a"^2)| + "c"`

= `log |"t" + sqrt("t"^2 - (sqrt(2))^2)| + "c"`

= `log |(x + 2) + sqrt((x + 2)^2 - 2)| + "c"`

= `log |(x + 2) + sqrt(x^2 + 4x + 4 - 2)| + "c"`

`int ("d"x)/sqrt(x^2 + 4x + 2) = log|(x + 2) + sqrt(x^2 + 4x + 2)| + "c"`

shaalaa.com

Is there an error in this question or solution?

Chapter 11: Integral Calculus - Exercise 11.10 [Page 219]

Chapter 11 Integral Calculus
Exercise 11.10 | Q 2. (iii) | Page 219

Find the volume of solid generated by rotating the area bounded by x²+y² =36 and the lines x = 0, x = 3 about X -axis.

Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.

Integrate the following functions with respect to x :

`(3x + 4) sqrt(3x + 7)`

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Integrate the following with respect to x :

`cot x/(log(sin x))`

Integrate the following with respect to x :

`("cosec" x)/(log(tan x/2))`