Advertisements
Advertisements
प्रश्न
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Advertisements
उत्तर
Let I=\[\int\]tan x . sec3x dx
Let sec x = t
⇒ sec x tan x dx = dt
\[ = \frac{\sec^3 x}{3} + C \left( \because x = \sec x \right)\]
APPEARS IN
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
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 : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
`int sqrt(1 + "x"^2) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int cot^2x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int x^3 e^(x^2) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int 1/(x(x-1))dx`
