put into partial fraction 1 / { (x^3) + 1 }

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partial fraction of 1 / { (x^3) + 1 } first factorise { (x^3) + 1 } using the identity for (a^3) +(b^3) the linear factor (x + 1) is grouped with A / (x + 1) the quadratic factor [ (x^2) - x + 1 ], which cannot be factored, is grouped with [ Bx+C ] / [ (x^2) - x + 1] simplify by getting rid of the denominator, put x = (-1) on both sides to get the value of A compare the coeffeicients of (x^2) and constant term to get equations involving B and C and solve for them.
integration formula--------------------------------------------problem2derivative of ln(x + sqrt(x^2-1))(x
+ sqrt(x^2-1)this is an example of differentiation using function of function or chain rule first use the derivative of ln(u) where u = then use the derivative of x + then the derivative of sqrt(v) where v =(x^2)-1 then finally the derivative of (x^2)-1 * list
of differentiation formula
some problems from integral calculus * Integrate
e^{x^(1/3)}dx* evaluate
integral of [e^(-x) +1] ^2* evaluate
∫ (sin 3x)^4 dx
with limits 0 to
pi* evaluate
the integral of sqrt(tan x)* evaluate
integral of { sqrt{1+(x^2)}
} / {x^2}
using
integration by parts* ∫
sec³x dx
using integration by parts* integral
of (e^(ax) ) cosbx
using integration by partsArea using integral* evaluate
the area of an ellipse (x²
/a²) + (y²/b²) =1 using
integration* find the area between y² = x and x² =y * find
the area bounded b y =x²
and y = 3xother questions and problems: * integral
calculus integration formula---------------------------------------------------------------------------------------------- trigonometric
identity and ratio of certain standard angles* list
of differentiation formula
*integral
calculus integration formula--------------------------------------------------------------------------------------- |

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