Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Advertisements
उत्तर
Let I = `int(7 + 4x +5x^2)/(2x + 3)^(3/2).dx`
= `int(5x^2 + 4x + 7)/(2x + 3)^(3/2).dx`
Put 2x + 3 = t
∴ 2dx = dt
∴ dx = `dt/(2)`
Also, x = `(t - 3)/(2)`
∴ I = `int(5((t - 3)/2)^2 + 4((t - 3)/2) + 7)/t^(3/2).dt/(2)`
= `(1)/(2) int(5((t^2 - 6t + 9)/4) + 2(t - 3) + 7)/t^(3/2)dt`
= `(1)/(2)int (5t^2 - 30t + 45 + 8t - 24 + 28)/(4t^(3/2))dt`
= `(1)/(8)int(5t^2 - 22t + 49)/t^(3/2)dt`
= `(1)/(8)int(5t^(1/2) - 22t^(-1/2) + 49t^(-3/2))dt`
= `(5)/(8)intt^(1/2)dt - 22/8 int t^(-1/2)dt + 49/8 int t^(-3/2)dt`
= `(5)/(8).t^(3/2)/((3/2)) - (11)/(4).t^(1/2)/((1/2)) + (49)/(8).t^(-1/2)/((-1/2)) + c`
= `(5)/(12)(2x+ 3)^(3/2) - (11)/(2)sqrt(2x + 3) - (49)/(4).(1)/sqrt(2x + 3) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals:
tan2x dx
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/(cos x - sin x)` dx = _______________
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
`int x^3 e^(x^2) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
What must be done before integrating after obtaining \[du\]?
