Evaluate the integrals. ∫x(x+3)10dx

Pearl Carney

Pearl Carney

Answered question

2021-11-19

Evaluate the integrals.
x(x+3)10dx

Answer & Explanation

Parminquale

Parminquale

Beginner2021-11-20Added 17 answers

Step 1
According to the question, we have to integrate the given integral x(x+3)10dx.
The given integral is indefinite integral and this type of integration have no fixed value that is why we add a constant value after the integration.
To solve the above integral, we have to use the power formula, which is given as follows,
xndx=xn+1n+1+C
Step 2
Rewrite the given integral,
x(x+3)10dx
Now,
Let, I=x(x+3)10dx...(1)
To solve further, we have to use substitution method, so substitutins x+3=t and proceeding as follows,
x+3=t...(1)
Differentiating both sides with respect to x, we get,
dx=dt
Now, substituting as x=(t−3) and dx=dt, in the equation (1), we get,
Step 3
I=(t3)t10dt
=t11dt3t10dt
=t12123t1111+C
Now, substitute back in the above answer as x+3=t,we get the final answer as,
I=(x+3)12123(x+3)1111+C
Sevensis1977

Sevensis1977

Beginner2021-11-21Added 15 answers

Step 1: Use Integration by Substitution.
Let u=x+3, du=dx then x dx=u-3du
Step 2: Using u and dudu above, rewrite x(x+3)10dx.
(u3)u10du
Step 3: Expand.
u113u10du
Step 4: Use Power Rule: xndx=xn+1n+1+C.
u12123u1111
Step 5: Substitute u=x+3 back into the original integral.
(x+3)12123(x+3)1111
Step 6: Add constant.
(x+3)12123(x+3)1111+C

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