Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Advertisements
Solution
Let I = `int (x.sec^2(x^2))/sqrt(tan^3(x^2)).dx`
Put tan(x2) = t
∴ sec2(x2) x 2x dx = dt
∴ `x.sec^2(x^2)dx = dt/(2)`
∴ I = `int (1)/sqrt(t^3).dt/(2)`
= `(1)/(2) int t^(-3/2)dt`
= `(1)/(2).(t^(-1/2))/(-1/2) + c`
= `(-1)/sqrt(t) + c`
= `(-1)/sqrt(tan(x^2)) + c`.
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
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`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int logx/x "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int cot^2x "d"x`
`int sin^-1 x`dx = ?
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int sec^6 x tan x "d"x` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int cos^3x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
