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Popular >

integral from 1 to 2 of 1/x-x

Solution

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

Solution

ln (2) - \frac{3}{2}

+1

Decimal Notation

- 0.80685 \dots

Solution steps

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

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

\int_{1}^{2} x d x = \frac{3}{2}

= ln (2) - \frac{3}{2}

Popular Examples

integral of cot(y)

\int cot (y) d y

limit as x approaches 0+of x(1-cos(1/x))

x \to 0 + lim (x (1 - cos (\frac{1}{x})))

integral of 1/(x^2*sqrt(x^2+4))

\int \frac{1}{x ^{2} \cdot x ^{2} + 4} d x

(dx)/(dt)-5x=sin(2t),x(0)=pi

\frac{d x}{d t} - 5 x = sin (2 t), x (0) = π

integral of tan^5(3x)

\int tan^{5} (3 x) d x

Frequently Asked Questions (FAQ)

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