What is the integral from 3 to 5 of 80-(240)/(x+4) ?

The integral from 3 to 5 of 80-(240)/(x+4) is 160-240(2ln(3)-ln(7))

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integral from 3 to 5 of 80-(240)/(x+4)

\int_{3}^{5} 80 - \frac{240}{x + 4} d x

160 - 240 (2 ln (3) - ln (7))

Decimal

99.68453 \dots

Solution steps

\int_{3}^{5} 80 - \frac{240}{x + 4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{3}^{5} 80 d x - \int_{3}^{5} \frac{240}{x + 4} d x

\int_{3}^{5} 80 d x = 160

\int_{3}^{5} \frac{240}{x + 4} d x = 240 (2 ln (3) - ln (7))

= 160 - 240 (2 ln (3) - ln (7))

\int_{0}^{3} - 10 x d x

\int_{0}^{5} t e^{- s t} d t

\int_{1}^{9} 8 u d u

\int_{0}^{9} 2 d x

\int_{1}^{9} \frac{1}{16 + ( x + 3 ) ^{2}} d x

What is the integral from 3 to 5 of 80-(240)/(x+4) ?
The integral from 3 to 5 of 80-(240)/(x+4) is 160-240(2ln(3)-ln(7))