What is the integral from 1 to 4 of 3x^2-1/x ?

The integral from 1 to 4 of 3x^2-1/x is 63-2ln(2)

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integral from 1 to 4 of 3x^2-1/x

\int_{1}^{4} 3 x^{2} - \frac{1}{x} d x

63 - 2 ln (2)

Decimal Notation

61.61370 \dots

Solution steps

\int_{1}^{4} 3 x^{2} - \frac{1}{x} 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} 3 x^{2} d x - \int_{1}^{4} \frac{1}{x} d x

\int_{1}^{4} 3 x^{2} d x = 63

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

= 63 - 2 ln (2)

\int_{0}^{x} sin (x) d x

\frac{\partial}{\partial x} (2 y x^{2} - 3)

f (x) = x^{2} - 3 x + 2

\int_{0}^{1} 7 x e^{- x^{2}} d x

\frac{\partial}{\partial x} (x y^{2} + 7)

What is the integral from 1 to 4 of 3x^2-1/x ?
The integral from 1 to 4 of 3x^2-1/x is 63-2ln(2)