Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Advertisements
उत्तर
Let I = `int (e^x.log(sin e^x))/tan(e^x).dx`
= `int log (sin e^x).e^x.cot (e^x) dx`
Put log (sin ex) = t
∴ `(1)/sin (e^x).cos(e^x).e^x dx` = dt
∴ ex . cot (ex) dx = dt
∴ I = `int t dt = t^2/(2) + c`
= `(1)/(2)[log (sine^x)]^2 + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`1/(1 + cot x)`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
`int sqrt(1 + "x"^2) "dx"` =
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(1 + sin2x) dx`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int 1/(xsin^2(logx)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int sin^-1 x`dx = ?
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
Write `int cotx dx`.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Solve the following 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)
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
What is integration by substitution?
If \[x=g(t)\] and \[dx=g'(t)dt\], which formula represents integration by substitution?
When applying substitution, what must always be rewritten in terms of the new variable?
