Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\text{ Let I }= \int \frac{\cos x}{\sin x \cdot \log \sin x}dx\]
\[ \Rightarrow \int \frac{\cot x}{\log \sin x}dx\]
\[\text{ Let log sin x} = t\]
\[ \Rightarrow \text{ cot x dx} = dt\]
\[ \therefore I = \int \frac{dt}{t}\]
\[ = \text{ log t + C}\]
\[ = \text{ log}\left( \text{ log sin x} \right) + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
`int (dx)/(sin^2 x cos^2 x)` equals:
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`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 1/(sqrt(3"x"^2 - 5))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: ∫ |x| dx if x < 0
`int (7x + 9)^13 "d"x` ______ + c
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
`int 1/(sin^2x cos^2x)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`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
