Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Advertisements
उत्तर
Let I = `int cosx/sin(x - a).dx`
= `int cos[(x - a) + a]/sin(x - a).dx`
= `int[cos(x - a)cos a - sin(x - a)sin a)/sin(x - a).dx`
= `int [(cos(x - a)cos a)/sin(x - a) - (sin(x - a)sina)/sin(x - a)].dx`
= `cos a int cot (x - a)dx - sin a int 1 dx`
= cos a log |sin(x – a)| – x sin a + c.
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
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 "x - 1"/sqrt("x + 4")` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cos^7 x "d"x`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int cos^3x dx` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
