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 :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
cot x log sin x
Integrate the functions:
`(1+ log x)^2/x`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
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 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
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)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int logx/x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int(log(logx))/x "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int (1+x+x^2/(2!))dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int1/(x(x-1))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
