Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I= elog sin x . cos x dx
⇒ cos x dx = dt
\[= \frac{t^2}{2} + C\]
\[ = \frac{\sin^2 x}{2} + C \left( \because t = \sin x \right)\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
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 : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following:
`int (1)/(25 - 9x^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 (2x + 3)/(2x^2 + 3x - 1).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` 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 sqrt(1 + "x"^2) "dx"` =
`int logx/x "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following
`int x^3 e^(x^2) ` dx
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
After choosing \[u=g(x)\], what is the next step?
