Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
उत्तर
Let I = `int tan 3x tan 2x tanx dx`
Consider tan 3x = tan (2x + x)
= `(tan2x + tanx)/(1 - tan2x tanx)`
∴ tan3x (1 – tan 2x tan x) = tan 2x + tan x
∴ tan 3x – tan 3x tan 2x tan x = tan 2x + tan x
∴ tan 3x – tan 2x – tan x = tan 3x tan 2x tan x
I = `int (tan3x - tan 2x - tanx)dx`
= `int tan3xdx - int tan2x dx - int tanx dx`
= `(1)/(3)log|sec3x| - (1)/(2)log|sec2x| - log|secx| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int cos^7 x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int(5x + 2)/(3x - 4) dx` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int(log(logx) + 1/(logx)^2)dx` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int 1/(sinx.cos^2x)dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int (logx)^2/x dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
