What is the integral from 1 to 4 of 1/x-(2x-1) ?

The integral from 1 to 4 of 1/x-(2x-1) is 2ln(2)-12

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integral from 1 to 4 of 1/x-(2x-1)

\int_{1}^{4} \frac{1}{x} - (2 x - 1) d x

2 ln (2) - 12

Decimal Notation

- 10.61370 \dots

Solution steps

\int_{1}^{4} \frac{1}{x} - (2 x - 1) d x

Simplify

= \int_{1}^{4} \frac{1}{x} - 2 x + 1 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_{1}^{4} \frac{1}{x} d x - \int_{1}^{4} 2 x d x + \int_{1}^{4} 1 d x

\int_{1}^{4} \frac{1}{x} d x = 2 ln (2)

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} 1 d x = 3

= 2 ln (2) - 15 + 3

Simplify

= 2 ln (2) - 12

\int_{3}^{0} 5 x - x^{3} d x

\int_{3}^{7} \frac{x}{x - 7} d x

\int_{0}^{3} x^{2} + 1 d x

\int_{0}^{1} 12 x (1 - x)^{2} d x

\int_{0}^{1} 4 x e^{7 x} d x

What is the integral from 1 to 4 of 1/x-(2x-1) ?
The integral from 1 to 4 of 1/x-(2x-1) is 2ln(2)-12