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Popular >

integral of 1/x+2x

Solution

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

Solution

ln ∣ x ∣ + x^{2} + C

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ + x^{2}

Add a constant to the solution

= ln ∣ x ∣ + x^{2} + C

Graph

Popular Examples

(\partial)/(\partial x)(4sin(4x))

\frac{\partial}{\partial x} (4 sin (4 x))

derivative of arccos(x+y)

\frac{d}{d x} (arccos (x + y))

tangent of f(x)=3x^2,\at x=(6)tangent of

f (x) = 3 x^{2}, at x = (6)

limit as x approaches 1+of 1/(x^3-1)

x \to 1 + lim (\frac{1}{x ^{3} - 1})

derivative of f(x)=tan^3(x)derivative of

f (x) = tan^{3} (x)

Frequently Asked Questions (FAQ)

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