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
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
cot x log sin x
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) 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\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int cos^2x.dx`
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:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(1 + sin2x) dx`
`int1/(4 + 3cos^2x)dx` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int cos^3x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
