Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Advertisements
उत्तर
Let I = `int (x.sec^2(x^2))/sqrt(tan^3(x^2)).dx`
Put tan(x2) = t
∴ sec2(x2) x 2x dx = dt
∴ `x.sec^2(x^2)dx = dt/(2)`
∴ I = `int (1)/sqrt(t^3).dt/(2)`
= `(1)/(2) int t^(-3/2)dt`
= `(1)/(2).(t^(-1/2))/(-1/2) + c`
= `(-1)/sqrt(t) + c`
= `(-1)/sqrt(tan(x^2)) + c`.
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int 1/(x(x-1)) dx`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : tan2x dx
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
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:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Evaluate `int 1/((2"x" + 3))` dx
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int dx/(1 + e^-x)` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
