Integration techniques. Use the methods introduced evaluate the following integrals. ∫3xx+4dx

William Cleghorn

William Cleghorn

Answered

2021-12-28

Integration techniques. Use the methods introduced evaluate the following integrals.
3xx+4dx

Answer & Explanation

vicki331g8

vicki331g8

Expert

2021-12-29Added 37 answers

Step 1
Given integral is
I=3xx+4dx
We will use the substitution method to solve the given integral.
Let x+4=t,...(i)
Taking square on both sides.
x+4=t2
x=t24
Differentiate (i) with respect to x.
12x+4=dtdx
dxx+4=2dt
Step 2
On substituting x=t24 and dxx+4=2dt in given integral, we get
I=3(t24)2dt
=6(t24)dt+C
=6[t334t]+C
=2t324t+C
Putting t=x+4, we get
I=2(x+4)324x+4+C
I=2(x+4)3224x+4+C
Step 3
Answer: The value of the given integral is I=2(x+4)3224x+4+C.

Thomas White

Thomas White

Expert

2021-12-30Added 40 answers

3xx+4dx
We make the change of variables:
x+4=t2
Therefore:
x=t24
dx=2tdt
3t212t2tdt
Simplify the fractional expression:
(6t224)dt
(6t224)dt=2t324t
Substituting instead of t=x+4, we get:
I=2(x+4)3224x+4+C

karton

karton

Expert

2022-01-04Added 439 answers

3xx+4dx3t12tdt3t12t12dt3tt1212t12dt3t12dt12t12dt2tt24t2(x+4)x+424x+42(x+4)x+424x+4+C

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