Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I= \[\int\] tan6 x . sec2 x dx
sec2 x dx = dt
\[= \frac{t^7}{7} + C\]
\[ = \frac{\tan^7 x}{7} + C \left( \because t = \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
The value of \[\int\frac{1}{x + x \log x} dx\] is
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following : `int (logx)2.dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate: `int "e"^sqrt"x"` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sin^-1 x`dx = ?
`int dx/(1 + e^-x)` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int 1/(sin^2x cos^2x)dx` = ______.
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1))dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?
