Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I=\[\int\] tan3 x . sec2 x dx
⇒ sec2x dx = dt
\[ = \frac{\tan^4 x}{4} + C \left( \because t = \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int log ("x"^2 + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int(1 - x)^(-2) dx` = ______.
Evaluate `int(3x^2 - 5)^2 "d"x`
`int1/(4 + 3cos^2x)dx` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
