Find the indefinite integral of \int (5-5^{x}+x^{5})dx

pro4ph5e4q2

pro4ph5e4q2

Answered question

2021-11-19

Find the indefinite integral of (55x+x5)dx

Answer & Explanation

Feas1981

Feas1981

Beginner2021-11-20Added 16 answers

Step 1
We have to find the indefinite integral of the function:
(55x+x5)dx
We know the formula of integration,
xndx=xn+1n+1+C
dx=x+C
axdx=axln(a)+C
Where, C is an arbitrary constant.
Step 2
Applying above formula for the given integral, we get
(55x+x5)dx=5dx5xdx+x5dx
=5x5xln(5)+x5+15+1+C
=5x5xln(5)+x66+C
Hence, value of the indefinite integral is 5x5xln(5)+x66+C.
Opeance1951

Opeance1951

Beginner2021-11-21Added 26 answers

Step 1: Expand.
55x+x5dx
Step 2: Use Sum Rule: f(x)+g(x)dx=f(x)dx+g(x)dx.
5+x5dx5xdx
Step 3: Use Power Rule: xndx=xn+1n+1+C.
5x+x665xdx
Step 4: Use this property: axdx=axlna.
5x+x665xln5
Step 5: Add constant.
5x+x665xln5+C

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