Advertisements
Advertisements
Question
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
Options
`(1 - x)^(-1) + c`
`(1 + x)^(-1) + c`
`(1 - x)^(-1) - 1 + c`
`(1 - x)^(-1) + 1 + c`
Solution
`int(1 - x)^(-2)dx` = `bb(underline((1 - x)^(-1) + c))`.
Explanation:
`int(1 - x)^(-2)dx = ((1 - x)^(-2 + 1))/((-2 + 1)).d/dx(1 - x) + c`
= `(1 - x)^-1/((-1)).(0 - 1) + c`
= (1 – x)–1 + c
RELATED QUESTIONS
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `intsqrt(1 - 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 : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
Evaluate `int 1/("x"("x" - 1)) "dx"`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int 1/(x(x-1)) dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
