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Chapter 4: Q. 25 (page 404)

Indefinite integrals: Use integration formulas, algebra, and educated guess-and-check strategies to find the following integrals.

鈭�3sech2xdx

Short Answer

Expert verified

The solution is:3tanhx+C

Step by step solution

01

Given

The given integral is:鈭�3sech2xdx

02

To Find 

Use integration formulas, algebra, and educated guess-and-check strategies to find the given integral.

03

Calculation 

We take the constant out of the integral. Then we get a familiar integral expression:

鈭�3sech2xdx=3鈭�sech2xdx=3tanhx+C

Where, C = integrating constant.

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Most popular questions from this chapter

Given a simple proof that鈭�k=5n(ak+bk)=鈭�k=5nak+鈭�k=5nbk

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�0蟺鈥�sin2鈦�x+cos2鈦�xdx

Show by exhibiting a counterexample that, in general, 鈭�f(x)g(x)dx鈮�鈭�f(x)dx鈭�g(x)dx. In other words, find two functions f and g such that the integral of their quotient is not equal to the quotient of their integrals.

Consider the sequence A(1), A(2), A(3),.....,A(n) write our the sequence up to n. What do you notice?

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value.

limn鈫�鈭�鈭�k=1nk2+k+1n
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