Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Advertisements
उत्तर
Let I = `int sqrt(x^2 + 2x + 5).dx`
= `int sqrt(x^2 + 2x + 1 + 4)dx`
= `int sqrt((x + 1)^2 + 2^2).dx`
= `((x + 1)/2) int sqrt((x + 1)^2 + 2^2) + 2^2/(2)log|(x + 1) + sqrt((x + 1)^2 + 2^2)| + c`
= `((x + 1)/2)sqrt(x^2 + 2x + 5) + 2log|(x + 1) + sqrt(x^2 + 2x + 5)| + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin x.
Integrate the function in `x^2e^x`.
Integrate the function in x cos-1 x.
Integrate the function in (sin-1x)2.
Integrate the function in x sec2 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : e2x sin x cos x
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int 1/(4x + 5x^(-11)) "d"x`
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Find: `int e^x.sin2xdx`
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`intcos^-1(sqrt(x))dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3e^(x^2) dx`
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Which pair is listed as Exponential in the LIATE rule?
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]
Repeated parts may be needed for which pair of integrals?
