Antiderivatives

$⊳$ Antiderivatives and indefinite integrals (3:42) What is the antiderivative of $2 x$ ?
* Practice: antiderivatives and indefinite integrals (4 problems)
$⊳$ Reverse power rule (5:47) Deriving $\int x^{n} d x$ followed by finding $\int x^{5} d x$ and $\int 5 x^{- 2} d x$ .
* Practice: Reverse power rule. (4 problems)
* Practice: Reverse power rule with negative and fractional powers. (4 problems)
$⊳$ Indefinite integrals: sums and multiples (4:55) The indefinite integral of a sum and a multiple of a function. Find $\int (x^{2} + \cos x) d x$ and $\int (π \cos x) d x$ .
* Practice: Reverse power rule with sums and multiples. (4 problems)
$⊳$ Rewriting before integration (5:16) Find $\int x^{2} (3 x - 1) d x$ , $\int \frac{x^{3} + 3 x^{2} - 5}{x^{2}} d x$ , $\int {\sqrt[3]{x}}^{5} d x$ .
* Practice: Reverse power rule: rewriting before integrating. (4 problems)
$⊳$ Indefinite integrals of $\sin (x)$ , $\cos (x)$ and $e^{x}$ (4:03) Find $\int (\sin t + \cos t) d t$ and $\int (e^{a} + \frac{1}{a}) d a$ .
* Practice: Indefinite integrals: $e^{x}$ and $\frac{1}{x}$ . (4 problems)
* Practice: Indefinite integrals: $\sin x$ and $\cos x$ . (4 problems)

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The OpenLab at City Tech:A place to learn, work, and share

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