Advertisements
Advertisements
प्रश्न
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Advertisements
उत्तर
Let I = `int tan^2x sec^4 x"d"x`
= `int tan^2x sec^2x sec^2 x"d"x`
= `int tan^2x (1 + tan^2x)sec^2 x"d"x`
Put tan x = t
⇒ `sec^2x "d"x` = dt
∴ I = `int "t"^2(1 + "t"^2)"dt"`
= `int("t"^2 + "t"^4)"dt"`
= `"t"^3/3 + "t"^5/5 + "C"`
= `(tan^5x)/5 + (tan^3x)/3 + "C"`
APPEARS IN
संबंधित प्रश्न
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find the integrals of the function:
sin−1 (cos x)
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Find `int dx/(x^2 + 4x + 8)`
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ sin ("x" - a)/(sin ("x" + a )) 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"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
What does integration using trigonometric identities mean?
Which identity is used for an even power of cosine?
Which identity is used for the product of sine and cosine?
What is \(\int \cos^2 x\,dx\)?
