Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Advertisements
उत्तर
Let I = e3logx(x4 + 1)–1.dx
= `int e^(logx^3)/(x^4 + 1).dx`
= `int x^3/(x^4 + 1).dx` ...[∵ elogN = N]
= `(1)/(4) int(4x^3)/(x^4 + 1).dx`
= `(1)/(4) int(d/dx(x^4 + 1))/(x^4 + 1).dx`
= `(1)/(4)log|x^4 + 1| + c. ...[∵ int (f'(x))/f(x) dx = log|f(x)| + c]`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Evaluate the following integrals: `int sin 4x cos 3x dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : sin5x.cos8x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: `int log ("x"^2 + "x")` dx
`int 1/(cos x - sin x)` dx = _______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int sqrt(1 + sin2x) dx`
`int 1/(xsin^2(logx)) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
`int cos^3x dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
