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Popular >

integral of 1/x+x

Solution

\int \frac{1}{x} + x d x

Solution

ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Solution steps

\int \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 \frac{1}{x} d x + \int x d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int x d x = \frac{x ^{2}}{2}

= ln ∣ x ∣ + \frac{x ^{2}}{2}

Add a constant to the solution

= ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Popular Examples

y^{^{'}} - 6 y = 0

(\partial)/(\partial x)(x^{0.2}*y^{0.8})

\frac{\partial}{\partial x} (x^{0.2} \cdot y^{0.8})

integral of 4cos(x-1)

\int 4 cos (x - 1) d x

integral of 1/(sqrt(x^2+2x+17))

\int \frac{1}{x ^{2} + 2 x + 17} d x

integral of csc(1)

\int csc (1) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/x+x ?
The integral of 1/x+x is ln|x|+(x^2)/2+C