Advertisements
Advertisements
Questions
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Evaluate:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Advertisements
Solution
Given: `int (x^3 - x^2 + x - 1)/(x - 1) dx`
= `int (x^2 (x - 1) + 1(x - 1))/((x - 1)) dx`
= `int ((x - 1) (x^2 + 1))/((x - 1)) dx`
= `int (x^2 + 1) dx`
= `int x^2 dx + int 1 dx`
= `x^3/3 + x + c`
APPEARS IN
RELATED QUESTIONS
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(2x^2 + e^x)dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (xdx)/((x - 1)(x - 2))` equals
`int x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
What is anti derivative of `e^(2x)`
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
