Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`
Advertisements
उत्तर
Let I = `int sqrt(5x^2 + 3).dx`
= `sqrt(5) int sqrt(x^2 + 3/5).dx`
= `sqrt(5) [x/2 sqrt(x^2 + 3/5) + ((3/5))/(2)log|x + sqrt(x^2 + 3/5)|] + c`
= `sqrt(5)/(2) [x sqrt(x^2 + 3/5) + (3)/(5)log|x + sqrt(x^2 + 3/5)|] + c`.
APPEARS IN
संबंधित प्रश्न
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x2 log x.
Integrate the function in x tan-1 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `(xe^x)/(1+x)^2`.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
`int logx/(1 + logx)^2 "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
`int 1/sqrt(x^2 - a^2)dx` = ______.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`inte^(xloga).e^x dx` is ______
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int (logx)^2 dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int x^2 cos x dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Which differentiation identity verifies the special integral \[\int e^x\left[f(x)+f'(x)\right]dx=e^xf(x)+C?\]
When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?
Repeated parts may be needed for which pair of integrals?
