Mathematics, 21.03.2021 09:10 chels8547

Please help if you know how to integrate using substitution.

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Answer from: Happypuppy1918

B. $\displaystyle \frac{-1}{2}ln|cos2x| + C$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Calculus

Antiderivatives - Integrals

Integral Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {tan(u)} \, du = -ln|cosu| + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {tan(2x)} \, dx$

Step 2: Identify Variables

Set variables for u-substitution.

u = 2x

du = 2dx

Step 3: Integrate

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \frac{1}{2}\int {2tan(2x)} \, dx$ [Integral] U-Substitution: $\displaystyle \frac{1}{2}\int {tanu} \, du$ [Integral] Trig Integration: $\displaystyle \frac{1}{2}(-ln|cosu|) + C$ [Integral] Back-Substitute: $\displaystyle \frac{-1}{2}ln|cos2x| + C$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

Why are u not just putting the numbers this is to much

Answer from: Quest

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

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Please help if you know how to integrate using substitution.
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