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Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).

Short Answer

Expert verified

Thethree integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x) is8xx2+1dx,13x+1dxandex2-exdx.

Step by step solution

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Step 1. Given Information

Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).

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Step 2. The first integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x) 

8xx2+1dx

In his integration if we choose x2+1=uthen dudx=2x, so 12du=xdx. We can write the integral as 8xx2+1dx=82duu=4duuwhich we know how to integrate.

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Step 3. The second integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x) 

13x+1dx

In his integration if we choose 3x+1=uthen dudx=3, so role="math" 13du=dx. We can write the integral as role="math" localid="1648788212772" 13x+1dx=131uduwhich we know how to integrate.

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Step 4. The third integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x) 

ex2-exdx

In his integration if we choose 2-ex=uthen dudx=-ex, so -du=exdx. We can write the integral as ex2-exdx=-1uduwhich we know how to integrate.

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