Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Advertisements
उत्तर
`int (3x + 4) sqrt(3x + 7) "d"x = int (3x + 7 - 3) sqrt(3x + 7) "d"x`
= `int [(3x + 7) sqrt(3x + 7) - 3sqrt(3x + 7)] "d"x`
= `int (3x + 7) sqrt(3x + 7) "d"x - int 3sqrt(3x + 7) "d"x`
= `int (3x + 7)^(3/2) "d"x - 3int (3x + 7)^(1/2) "d"x`
= `1/3 (3x + 7)^(3/2 + 1)/(3/2 + 1) - 3(3x + 7)^(1/2 + 1)/(1/2 + 1) + "c"`
= `1/3 (3x + 7)^(5/2)/(5/2) - 3 xx 1/3 (3x + 7)^(3/2)/(3/2) + "c"`
= `1/3 xx 2/5 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
= `2/15 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.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.
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
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 sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
