The antiderivative rules in calculus are basic rules that are used to find the antiderivatives of different combinations of functions.
Find the antiderivative of the function: f(x) = \frac{1}{x^2} + x Find the antiderivative of the function: x6 - 1 over x6 Find the antiderivative of the function f(x) = \frac{x^5 - x^3 + 6x}{x^4} Find an antiderivative of the function f(x) = 8x^3 -...
Determine an antiderivative, y, of the given derivative, y'. Then use the given condition on y to determine the constant of integration. \frac{dy}{dx}=2x^{-2}+3x^{-1}-6; y(1)=5. Determine an antiderivative y , of the given derivative, y' ....
Find the antiderivative: y = \frac{2}{5} \csc^2 (\frac{x}{5}) Solve the following antiderivative: integral of 1/((1 + x^2)((arctan x)^2 + 2arctan x + 1)) dx. Find the antiderivative for f(x) = \frac{2x^2 + x + 9}{(x - 1)(x^2 + 3)} ...
f(x) = \frac{6}{5}csc^2 (\frac{x}{5}) Find the antiderivative. f(u) = u^3 - 2u + sqrt(u). Find the antiderivative: int dfrac{1}{10+x^2+2x} dx. Find the antiderivative. f(x) = x + 12x2 Find the antiderivative of 7x^3. Find the antiderivative. f(x) = (x...
The integrands having a polynomial function are evaluated using the power rule of anti-derivatives. The mathematical expression for the power rule is as follows: ∫xk dx=xk+1k+1+C Answer and Explanation: 1 Given: P′(x)=−80x2; P(6)=4 Using the concep...
Find the particular antiderivative of the following derivative that satisfies the given condition. {eq}\frac{dy}{dx} = 5x^{-4} + 4x^{-1} - 1;y(1) = 5. {/eq} y(x) = Solution of the Differential Equation : We can solve this by sep...
Find the particular antiderivative of the following derivative that satisfies the given condition. dydx=2x−4+5x−1−1;y(1)=1 Anti-Differentiation Integration is also known as anti-differentiation as differentiation is nothing but the inverse function...
f(x)=2x2+x+6x, f(1)=3 Antiderivatives: The indefinite integrals, also known as the antiderivatives came into existence in the 1700s. They are just the reverse of the derivatives. We usually see the applications of the antiderivatives while evaluating the definite integrals ...