Integration Immediately!

Calculus Level 2

Compute the following definite integral

∫ 1 5 ( 17 x + 3 ) d x \displaystyle\int_{1}^{5}(\dfrac{17}{x}+3)dx

If the answer can be expressed in a ln ⁡ b + c a \ln b + c , where a , b , c a, b, c are positive integers, then find the product a b c abc .


The answer is 1020.

Danushan Dayaparan by Danushan Dayaparan , 20, Singapore

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1 solution

Since an antiderivative for the integral is 17 ln ⁡ ∣ x ∣ + 3 x 17\ln|x|+3x , we can immediately apply the Newton-Leibnitz Formula to get: ∫ 1 5 ( 17 x + 3 ) d x \displaystyle\int_{1}^{5}(\dfrac{17}{x}+3)dx = 17 ln ⁡ 17\ln + \dfrac{3x}{1}\right|_1^5 = 17 ln ⁡ 5 + 15 − 3 17\ln5 +15 - 3 = 17 ln ⁡ 5 + 12 17\ln5 + 12

Therefore, 17 ∗ 5 ∗ 12 = 1020 17*5*12 = 1020

4 Helpful 0 Interesting 0 Brilliant 0 Confused

sorry about the code in the middle

Danushan Dayaparan - 6 years, 10 months ago

My LaTeX isnt very strong even though i was refrring to Daniel Liu's beginner guide to LaTeX

Danushan Dayaparan - 6 years, 10 months ago

how do you write the mathematical functions like integration sign?

samarth sangam - 6 years, 9 months ago

I recommend checking Daniel Liu's Basic Guide to LaTeX! That's where I learnt me basics

Danushan Dayaparan - 6 years, 9 months ago

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