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

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 : `int1/(x(3+logx))dx`

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.

Integrate the following functions with respect to x :

`(cos2x - cos 2 alpha)/(cosx - cos alpha)`

Integrate the following functions with respect to x :

`(sin^2x)/(1 + cosx)`

Integrate the following functions with respect to x :

`"e"^(x log "a") "e"^x`

Integrate the following functions with respect to x :

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

Integrate the following with respect to x :

`x^2/(1 + x^6)`

Integrate the following with respect to x :

`(sin^-1 x)/sqrt(1 - x^2)`

Integrate the following with respect to x:

`"e"^(- 3x) sin 2x`

Integrate the following with respect to x:

`(2x - 3)/(x^2 + 4x - 12)`

Integrate the following with respect to x:

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

Integrate the following functions with respect to x:

`sqrt(9 - (2x + 5)^2`

Integrate the following functions with respect to x:

`sqrt(81 + (2x + 1)^2`