Advertisements
Advertisements
प्रश्न
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Advertisements
उत्तर
Let I = `int (10x^9 + 10^x.log10)/(10^x + x^10).dx`
Put 10x + x10 = t
∴ (10x. log 10 + 10x9).dx = dt
∴ I = `int(1)/t dt` = log | t | + c
= log | 10x + x10 | + c
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x^x (1 + logx) "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int ("d"x)/(x(x^4 + 1))` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
After choosing \[u=g(x)\], what is the next step?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
