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Popular >

integral of 2x+3x^{-2}

Solution

\int 2 x + 3 x^{- 2} d x

Solution

x^{2} - \frac{3}{x} + C

Solution steps

\int 2 x + 3 x^{- 2} d x

3 x^{- 2} = \frac{3}{x ^{2}}

= \int 2 x + \frac{3}{x ^{2}} 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 2 x d x + \int \frac{3}{x ^{2}} d x

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

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

= x^{2} - \frac{3}{x}

Add a constant to the solution

= x^{2} - \frac{3}{x} + C

Popular Examples

integral of (5sin^3(sqrt(x)))/(sqrt(x))

\int \frac{5 sin ^{3} ( x )}{x} d x

(dy)/(dt)+2y=3e^t,y(0)=1

\frac{d y}{d t} + 2 y = 3 e^{t}, y (0) = 1

derivative of y=ln(x^4)derivative of

y = ln (x^{4})

integral of sqrt(4+5x^2)

\int 4 + 5 x^{2} d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of 2x+3x^{-2} ?
The integral of 2x+3x^{-2} is x^2-3/x+C