Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Advertisements
उत्तर
I = `int1/sqrt(3x^2 + 5x + 7)dx`
I = `1/sqrt3 int 1/sqrt(x^2 + (5x)/3 + 7/3)dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + 25/36) + (7/3 - 25/36))dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + (5/6)^2) + (59/36)).dx`
I = `1/sqrt3 int 1/sqrt((x + 5/6)^2 + (sqrt59/6)^2)dx`
I = `1/sqrt3 log |(x + 5/6) +sqrt((x + 5/2)^2 + (sqrt59/6)^2)| + c` ....`int1/sqrt(x^2 + a^2)dx = log|x + sqrt(x^2 + a^2)| + c`
I = `1/sqrt3 . log|(x + 5/6) + sqrt(x^2 + (5x)/3 + 7/3)| + c`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int logx/x "d"x`
`int (cos2x)/(sin^2x) "d"x`
`int sin^-1 x`dx = ?
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Write `int cotx dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
