Advertisements
Advertisements
Question
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Advertisements
Solution
`int (2x - 7)/sqrt(4x - 1).dx`
= `(1)/(2)int(2(2x - 7))/sqrt(4x - 1).dx`
= `(1)/(2)int((4x - 1) - 13)/sqrt(4x - 1).dx`
= `(1)/(2)int(((4x - 1))/sqrt(4x - 1) - 13/sqrt(4x - 1)).dx`
= `(1)/(2)int (4x - 1)^(1/2).dx - 13/2 int(4x - 1)^(-1/2).dx`
= `(1)/(2)((4x - 1)^(3/2))/((4)(3/2)) - (13)/(2).((4x - 1)^(1/2))/((4)(1/2)) + c`
= `(1)/(12)(4x - 1)^(3/2) - (13)/(4)sqrt(4x - 1) + c`
RELATED QUESTIONS
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`e^(2x+3)`
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following functions w.r.t. x : `(logx)^n/x`
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 : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate `int 1/((2"x" + 3))` dx
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int x^3"e"^(x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
How should a substitution be chosen?
