Advertisements
Advertisements
Question
Evaluate the following integrals : tan2x dx
Solution
`int tan^2x dx = int(sec^2x - 1)dx`
= `int sec^2x dx - int 1. dx`
= tan x – x + c.
APPEARS IN
RELATED QUESTIONS
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Solve: dy/dx = cos(x + y)
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
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 (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int cos^2x.dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
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:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int cos sqrtx` dx = _____________
`int (log x)/(log ex)^2` dx = _________
`int sqrt(1 + sin2x) "d"x`
`int logx/x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int sin^-1 x`dx = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
`int sec^6 x tan x "d"x` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int cos^3x dx` = ______.
Write `int cotx dx`.
`int (logx)^2/x dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(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).