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Popular >

integral of 2x+8e^x

Solution

\int 2 x + 8 e^{x} d x

Solution

x^{2} + 8 e^{x} + C

Solution steps

\int 2 x + 8 e^{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 2 x d x + \int 8 e^{x} d x

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

\int 8 e^{x} d x = 8 e^{x}

= x^{2} + 8 e^{x}

Add a constant to the solution

= x^{2} + 8 e^{x} + C

Popular Examples

(dy)/(dt)= 4/5 y

\frac{d y}{d t} = \frac{4}{5} y

derivative of (0.09(5^x)/(x^3))

\frac{d}{d x} (\frac{0.09 ( 5 ^{x} )}{x ^{3}})

derivative of ln((3x/4))

\frac{d}{d x} (ln (\frac{3 x}{4}))

y^'=(x(x^2+1))/(4y^3)

y^{^{'}} = \frac{x ( x ^{2} + 1 )}{4 y ^{3}}

integral of 3/(x^4)+4/(x^2)-6/(x^3)

\int \frac{3}{x ^{4}} + \frac{4}{x ^{2}} - \frac{6}{x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of 2x+8e^x ?
The integral of 2x+8e^x is x^2+8e^x+C