Advertisements
Advertisements
Question
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Advertisements
Solution
We are asked to evaluate:
`int(x-2)/sqrt(x+5) dx`
u = x + 5
`(du)/dx = 1 => du=dx`
x = u − 5
`int ((u-5)-2)/sqrtu du = int (u-7)/sqrtu du`
`= int (u/sqrtu-7/sqrtu)du`
`int (u^(1/2)-7u^(-1/2)) du`
`int u^(1/2) du = u^(3/2)/(3/2) = 2/3 u^(3/2)`
`int u^(-1/2) du = u^(1/2)/(1/2) = 2u^(1/2)`
`= 2/3 u^(3/2) - 7(2u^(1/2))`
`= 2/3 u^(3/2) - 14(u^(1/2))`
`= 2/3 (x+5)^(3/2) - 14(x+5)^(1/2) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: ∫ |x| dx if x < 0
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Write `int cotx dx`.
Find `int dx/sqrt(sin^3x cos(x - α))`.
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 the following
`int1/(x^2 +4x-5)dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
What must be done before integrating after obtaining \[du\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
