Advertisements
Advertisements
Question
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Advertisements
Solution
`int (3 sec^2 x - 4/x + 1/(xsqrt(x)) - 7)dx`
= `3int sec^2x dx - 4 int 1/x dx + intx ^(-(3)/(2)) dx - 7 int 1 dx`
= `3 tan x - 4 log |x| + (x ^(- 3/2 + 1))/(-3/2 + 1) - 7x + c`
= `3 tan x - 4 log |x| + (x ^(- 1/2 ))/(-1/2) - 7x + c`
= `3 tan x - 4 log |x| + (-2x^(-1/2)) - 7x + c`
= `3tan x - 4 log |x| - 2/sqrt(x) - 7x + c`
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
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\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 1/(cos x - sin x)` dx = _______________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int x^3"e"^(x^2) "d"x`
`int sin^-1 x`dx = ?
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
`int x^3 e^(x^2) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
