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William Briggs, Lyle Cochran, Bernard Gillet

3 Edition

Chapter 8, Problem 67

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Integrals of cot $x$ and $\csc x$Prove that $\int \csc x \, d x=-\ln |\csc x+\cot x|+C$(Hint: See Example 2.)

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01:41

Integrals of cot $x$ and $\csc x$

Use a change of variables to prove that $\int \cot x \, d x=\ln |\sin x|+C$

(Hint: See Example $1 .$ )

06:25

Integrals of cot $x$ and $\csc x$

Prove that $\int \csc x d x=-\ln |\csc x+\cot x|+C$. (Hint: See the proof of Theorem 7.1.)

00:40

Integrals of $\cot x$ and $\csc x.$

Use a change of variables to prove that $\int \cot x \, d x=\ln |\sin x|+C.$

01:31

Integrals of cot $x$ and $\csc x$

Use a change of variables to prove that $\int \cot x d x=\ln |\sin x|+C$.

Transcript

so we need to prove the integral. Of course, seeking X DX is equal to minus Ln Cosi can’t X plus co tangent X plus C So we need to soft for the left side and proved that it’s equal to what we have here on the right side. So let’s start by multiplying. Cosi connects by Co Sequent X Plus Co. Tangent X, divided by co seeking X Plus Co Tangent X dear. So what will get here is co second squared, X Plus Co Seek and X Times Co Tangin X over co seek index plus co Tangent X dear. So from here, let’s take you as Cosi can’t X Plus co tangent fix Do you over DX is equal to minus Coast seeking squared X minus CO. 10 X Times Co seek index So do you r D X is equal to do you over minus co second squared x minus…