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Popular >

integral of 2x+9x^{-2}

Solution

\int 2 x + 9 x^{- 2} d x

Solution

x^{2} - \frac{9}{x} + C

Solution steps

\int 2 x + 9 x^{- 2} d x

9 x^{- 2} = \frac{9}{x ^{2}}

= \int 2 x + \frac{9}{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{9}{x ^{2}} d x

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

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

= x^{2} - \frac{9}{x}

Add a constant to the solution

= x^{2} - \frac{9}{x} + C

Popular Examples

y^'-1/x y=x^2y^4

y^{^{'}} - \frac{1}{x} y = x^{2} y^{4}

tangent of f(x)=3x^2-3x-5 tangent of

f (x) = 3 x^{2} - 3 x - 5

(\partial)/(\partial y)(x^4y^{-2})

\frac{\partial}{\partial y} (x^{4} y^{- 2})

integral of 1/((a^2-x^2)^{3/2)}

\int \frac{1}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} d x

integral from a to 2a of ax-(a^3)/x

\int_{a}^{2 a} a x - \frac{a ^{3}}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of 2x+9x^{-2} ?
The integral of 2x+9x^{-2} is x^2-9/x+C