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What's More Excercises: Determine the antiderivativ f(x)=(x+1)^(100)

What's More\newlineExcercises: Determine the antiderivativ\newline11. f(x)=(x+1)100 f(x)=(x+1)^{100}

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Q. What's More\newlineExcercises: Determine the antiderivativ\newline11. f(x)=(x+1)100 f(x)=(x+1)^{100}
  1. Power Rule Explanation: To find the antiderivative of f(x)f(x), we use the power rule for integration, which states that the antiderivative of xnx^n is x(n+1)n+1+C\frac{x^{(n+1)}}{n+1} + C, where CC is the constant of integration.
  2. Apply Power Rule to f(x)f(x): Apply the power rule to f(x)=(x+1)100f(x) = (x + 1)^{100}. Increase the exponent by 11 to get 101101 and divide by the new exponent.\newlineThe antiderivative of f(x)f(x) is (x+1)101101+C\frac{(x + 1)^{101}}{101} + C.

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