Advertisements
Advertisements
प्रश्न
Find `int dx/(x^2 + 4x + 8)`
Advertisements
उत्तर
Consider the integral, `int dx/(x^2 + 4x + 8)`
I = `int 1/(x^2 + 4x + 8)` dx
= `int 1/(x^2 + 4x + 4 + 4)` dx
= `int 1/((x + 2)^2 + 2^2) dx` {Use Intergral Formula : `int 1/(x^2 + a^2) dx = 1/a tan^(-1) (x/a)}`
`= 1/2 tan^(-1) (x + 2)/2 + C`
APPEARS IN
संबंधित प्रश्न
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`(cos 2x+ 2sin^2x)/(cos^2 x)`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Find `int_ (log "x")^2 d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sin^-1 (2x) dx.`
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
What does integration using trigonometric identities mean?
Which identity is used for \(\cos^2 x\)?
Which identity is used for the product of sine and cosine?
Using \(\cos^2 x = \frac{1+\cos 2x}{2}\), which expression is equivalent to \(\int \cos^2 x\,dx\)?
What is \(\int \cos^2 x\,dx\)?
Applying the product-to-sum identity to \(\sin 2x\cos 3x\) gives which expression?
Which procedure is recommended when an identity can simplify a complicated trigonometric expression?
