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Popular >

integral of e+e^{3x}

Solution

\int e + e^{3 x} d x

Solution

e x + \frac{1}{3} e^{3 x} + C

Solution steps

\int e + e^{3 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 e d x + \int e^{3 x} d x

\int e d x = e x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= e x + \frac{1}{3} e^{3 x}

Add a constant to the solution

= e x + \frac{1}{3} e^{3 x} + C

Popular Examples

derivative of x^{-2}e^{2x}

\frac{d}{d x} (x^{- 2} e^{2 x})

integral of-1/((x+1)^2)

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

(x^2+1)(dy)/(dx)+3x(y-1)=0

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0

derivative of x/(tan(x))

\frac{d}{d x} (\frac{x}{tan ( x )})

inverse oflaplace (2e^{-2s})/(s(s+2)(s+3)^2)inverse laplace

\frac{2 e ^{- 2 s}}{s ( s + 2 ) ( s + 3 ) ^{2}}

Frequently Asked Questions (FAQ)

What is the integral of e+e^{3x} ?
The integral of e+e^{3x} is ex+1/3 e^{3x}+C