Which of the following explains the best way to start evaluating $$\int_{ }^{ }\cos^3x\ dx$$ ?

Write $$\cos^3x$$ as $$\cos^2x\cdot\cos x$$ , then as $$\left(1-\sin^2x\right)\cdot\cos x$$ .

Write $$\cos^3x$$ as $$\cos x\cdot\cos^2x$$ , then as $$\cos x\cdot\frac{1+\cos2x}{2}$$ .

Write $$\cos^3x$$ as $$\frac{1+\cos3x}{3}$$ .

Which best describes how to evaluate $$\int\tan^6x\sec^4x\ dx$$ ?

Write $$\tan^6x\sec^4x$$ as $$\tan^6x\cdot\sec^2x\cdot\sec^2x$$ , then as $$\tan^6x\left(1+\tan^2x\right)\sec^2x$$ . Use a u -sub with $$u=\tan x$$ .

Write $$\tan^6x\sec^4x$$ as $$\tan^2x\cdot\tan^4x\cdot\sec^4x$$ , then as $$\left(\sec^2x-1\right)\tan^4x\sec^4x$$ . Use a u -sub with $$u=\sec x$$ .

Write $$\tan^6x\sec^4x$$ as $$\tan^2x\cdot\tan^4x\cdot\sec^4x$$ , then as $$\left(\sec^2x-1\right)\tan^4x\sec^4x$$ . Use a u -sub with $$u=\tan x$$ .

Write $$\tan^6x\sec^4x$$ as $$\tan^6x\cdot\sec^2x\cdot\sec^2x$$ , then as $$\tan^6x\left(1+\tan^2x\right)\sec^2x$$ . Use a u -sub with $$u=\sec x$$ .

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Trigonometric Integrals

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Mathematics

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12th Grade

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Practice Problem

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Medium

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CCSS

HSF.TF.C.9

Standards-aligned

Aaron Smith

Used 22+ times

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8 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Use the Power Rule for Integrals to directly evaluate the integral.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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