Find the integrals of the following: 16x-7-x2

Find the integrals of the following:

`1/(6x - 7 - x^2)`

योग

`int 1/(6x - 7 - x^2) "d"x = int ("d"x)/(- 7 - x^2 + 6x)`

= `int ("d"x)/(- 7 - (x^2 - 6x))`

= `int ("d"x)/(- 7 - [(x - 3)^2 - 3^2]`

= `int ("d"x)/(- 7 - (x - 3)^2 + 9)`

= `int ("d"x)/(2 - (x - 3)^2`

= `int ("d"x)/((sqrt(2))^2 - (x - 3)^2)`

Put x – 3 = t, dx = dt

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

= `1/(2 xx (sqrt(2))) log |(sqrt(2) + "t")/(sqrt(2) - "t")| + "c"`

= `1/(2 xx sqrt(2)) log |(sqrt(2) + (x - 3))/(sqrt(2) - (x - 3))| + "c"`

shaalaa.com

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

अध्याय 11: Integral Calculus - Exercise 11.10 [पृष्ठ २१९]

अध्याय 11 Integral Calculus
Exercise 11.10 | Q 2. (i) | पृष्ठ २१९

Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`

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

Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx

Integrate the following functions with respect to x :

`1/((x - 1)(x + 2)^2`

Integrate the following functions with respect to x :

`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`

Integrate the following with respect to x :

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

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))`

Integrate the following with respect to x :

`(sin 2x)/("a"^2 + "b"^2 sin^2x)`