Advertisements
Advertisements
प्रश्न
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Advertisements
उत्तर
`int (2x - 7)/sqrt(4x - 1).dx`
= `(1)/(2)int(2(2x - 7))/sqrt(4x - 1).dx`
= `(1)/(2)int((4x - 1) - 13)/sqrt(4x - 1).dx`
= `(1)/(2)int(((4x - 1))/sqrt(4x - 1) - 13/sqrt(4x - 1)).dx`
= `(1)/(2)int (4x - 1)^(1/2).dx - 13/2 int(4x - 1)^(-1/2).dx`
= `(1)/(2)((4x - 1)^(3/2))/((4)(3/2)) - (13)/(2).((4x - 1)^(1/2))/((4)(1/2)) + c`
= `(1)/(12)(4x - 1)^(3/2) - (13)/(4)sqrt(4x - 1) + c`
संबंधित प्रश्न
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 + cot x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int \log_e x\ dx\].
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int 1/(cos x - sin x)` dx = _______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int x^x (1 + logx) "d"x`
`int(log(logx))/x "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int ("d"x)/(x(x^4 + 1))` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int 1/(x(x-1))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int 1/(x(x-1))dx`
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
