Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
Let I= \[\int\]sin3 x . cos x dx
⇒ cos x dx = dt
\[ = \frac{\sin^4 x}{4} + C \left( \because t = \sin x \right)\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int sin x/cos^2x dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int (cos x)/(1 - sin x) "dx" =` ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
