4.8: Antiderivatives

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May 15, 2024
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- 4.7: L'Hôpital's Rule
- Chapter 5: Integration

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Evaluate $\displaystyle \int 3\ dx$ .
Evaluate $\displaystyle \int 2x^3\ dx$ .
Evaluate $\displaystyle \int (4x + \sqrt{x})\ dx$ .
Evaluate $\displaystyle \int \cos x\ dx$ .
Evaluate $\displaystyle \int \left(\dfrac{2}{x^2} - \dfrac{x^2}{2}\right)\ dx$ .
Evaluate $\displaystyle \int \dfrac{3x^2 + 2}{x^2}\ dx$ .
Evaluate $\displaystyle \int \left(\sec x \tan x + \dfrac{4}{x}\right)\ dx$ .
Evaluate $\displaystyle \int (4\sin x - 3\sec^2 x)\ dx$ .
Evaluate $\displaystyle \int \dfrac{5x^4 + 3x^2 + 7}{x^3}\ dx$ .
Evaluate $\displaystyle \int (2e^x - 5x^{-5/2})\ dx$ .
Find the function $f$ with $f'(x) = x^{-2}$ and $f(2) = 3$ .
Find the function $g$ with $g'(x) = \sqrt{x} + x^2$ and $g(0) = 2$ .
Find the function $h$ with $h'(x) = \dfrac{1}{\pi} - 3\sec x\tan x$ and $h(\pi) = 7$ .
Find two possible functions $f$ such that $f''(x) = x^2 + 2$ .
Find two possible functions $g$ such that $g''(x) = e^x + \dfrac{1}{2x^2}$ .
Find two possible functions $h$ such that $h'''(x) = \sin x$ .

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