Advertisements
Advertisements
प्रश्न
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Advertisements
उत्तर
`int_-a^a 9^x/(1 + 9^x)dx`
Let 1 + 9x = u
On differentiating with respect to x.
`\implies` 9x . log 9 = `(du)/dx`
`\implies` 9x dx = `(du)/log9`
= `int_(1 + 9^-a)^(1 + 9^a) (du)/(log9.u)`
= `1/log9 . [log (u)]_(1 + 9^-a)^(1 + 9^a) + C`
= `1/log9 [log (1 + 9^a) - log (1 + 9^-a)] + C`
= `1/log9 [log ((1 + 9^a)/(1 + 9^-a))] + C`.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int(log(logx))/x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int x^3"e"^(x^2) "d"x`
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
