What is #\int (3x + 5) dx#?

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Answer 1 · 2017-10-20T00:04:52

#3/2x^2+5x+C#

Let #I=int(3x+5)dx#

Apply linerarity

#I=3intx^1dx + 5intx^0dx#

Apply #int x^n dx = x^(n+1)/(n+1) +C# to both terms

#I= 3 * x^2/2 + 5*x^1/1 +C#

#= 3/2x^2+5x+C#

Answer 2 · 2017-10-20T00:05:25

# int \ (3x+5) \ dx = (3x^2)/2 + 5x + C#

We use the power rule for integration:

# int \ x^n \ dx = x^(n+1)/(n+1) \ \ \ \ (+c) #

Hence:

# int \ (3x+5) \ dx = (3x^2)/2 + 5x + C#