Advertisements
Advertisements
Question
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Solution
`inte^x "cosec" x(1 - cot x)dx`
= `int e^x("cosec" x - "cosec" x . cot x)dx`
= `int e^x("cosec" x + (-"cosec" x . cot x))dx` ...`[∵ inte^x(f(x) + f^'(x))dx = e^xf(x) + c]`
= `e^x"cosec" x + c`
APPEARS IN
RELATED QUESTIONS
Integrate the function in (x2 + 1) log x.
`intx^2 e^(x^3) dx` equals:
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Integrate the following w.r.t.x : sec4x cosec2x
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find: `int e^x.sin2xdx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
