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