- $\rhd$ 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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The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.
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