Advertisements
Advertisements
Question
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Advertisements
Solution
`int (cos2x)/(sin^2x.cos^2x)dx`
= `int(cos^2x - sin^2x)/(sin^2x.cos^2x)dx`
= `int(1/sin^2x - 1/cos^2x)dx`
= `int "cosec"^2x dx - int sec^2 x dx`
= – cot x – tan x + c.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :`intxlogxdx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals:
tan2x dx
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
`int logx/(log ex)^2*dx` = ______.
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/("x" log "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/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sin^-1 x`dx = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
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 `int (1+x+x^2/(2!))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
