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Excercises: Determine the antiderivatives f(x)=(x+1)^(100)

Excercises: Determine the antiderivatives\newline11. f(x)=(x+1)100 f(x)=(x+1)^{100}

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Q. Excercises: Determine the antiderivatives\newline11. f(x)=(x+1)100 f(x)=(x+1)^{100}
  1. Recognize Power Rule: Recognize the general power rule for antiderivatives, which states that the antiderivative of xnx^n is (x(n+1))/(n+1)+C(x^{(n+1)})/(n+1) + C, where CC is the constant of integration.\newlineCalculate the antiderivative of (x+1)100(x+1)^{100}.\newlineAntiderivative: ((x+1)100+1)/(100+1)+C((x+1)^{100+1})/(100+1) + C
  2. Calculate Antiderivative: Simplify the expression.\newlineAntiderivative: (x+1)101101+C\frac{(x+1)^{101}}{101} + C

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