Evaluate the integrals. ∫x3ex4dx

kuvitia9f

kuvitia9f

Answered

2021-12-31

Evaluate the integrals.
x3ex4dx

Answer & Explanation

ambarakaq8

ambarakaq8

Expert

2022-01-01Added 31 answers

Step 1
Solution -
Given integral -
y=x3ex4dx
Let,
t=x4
differentiating on both sides w.r.t x,
dtdx=4x3
dt=4x3dx
dt4=x3dx
Step 2
Now substituting these values in the given integral,
y=14etdt
y=14[et]+C
where C is the constant.
Philip Williams

Philip Williams

Expert

2022-01-02Added 39 answers

Step 1
This problem can be solved using a u-substitution. Let u=x4. Then du=4x3dx.
x3ex4dx=eu4du=eu4+c=ex44+c
Result:
ex44+c

Vasquez

Vasquez

Expert

2022-01-07Added 457 answers

Step 1
Substitute Px4=u and 4x3dx=dux3dx=14du
x3ex4dx=14eudu=14eu+C
Substitute back u=x4
=14ex4+C
Result:
14ex4+C

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