What is the integral from 4 to 7 of 3+2ln(t+5) ?

The integral from 4 to 7 of 3+2ln(t+5) is 2ln(16777216/729)+3

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integral from 4 to 7 of 3+2ln(t+5)

\int_{4}^{7} 3 + 2 ln (t + 5) d t

2 ln (\frac{16777216}{729}) + 3

Decimal

23.08771 \dots

Solution steps

\int_{4}^{7} 3 + 2 ln (t + 5) d t

Apply the Sum Rule:

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

= \int_{4}^{7} 3 d t + \int_{4}^{7} 2 ln (t + 5) d t

\int_{4}^{7} 3 d t = 9

\int_{4}^{7} 2 ln (t + 5) d t = 2 (ln (\frac{16777216}{729}) - 3)

= 9 + 2 (ln (\frac{16777216}{729}) - 3)

Simplify

9 + 2 (ln (\frac{16777216}{729}) - 3) : 2 ln (\frac{16777216}{729}) + 3

= 2 ln (\frac{16777216}{729}) + 3

\int_{0}^{2} (2 x - 6) (4 x^{2} + 5) d x

\int_{2}^{5} 6 + cos (\frac{x}{10}) d x

\int_{0}^{1} 2 x + 4 d x

\int_{\frac{1}{2}}^{\frac{1}{3}} (cos (π x)) d x

\int_{0}^{1} 2 π x 1 + 4 x^{2} d x

What is the integral from 4 to 7 of 3+2ln(t+5) ?
The integral from 4 to 7 of 3+2ln(t+5) is 2ln(16777216/729)+3