Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I= \[\int\] tan6 x . sec2 x dx
sec2 x dx = dt
\[= \frac{t^7}{7} + C\]
\[ = \frac{\tan^7 x}{7} + C \left( \because t = \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
cot x log sin x
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int logx/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int dx/(1 + e^-x)` = ______
Write `int cotx dx`.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) 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).
