What is the integral of 1/3 e^x ?

The integral of 1/3 e^x is 1/3 e^x+C

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integral of 1/3 e^x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

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

Add a constant to the solution

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

ln (x), 2

y = 3 x^{\frac{3}{8}}

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

\int \frac{9 x}{( x + 3 ) ^{2}} d x

\int (\frac{2}{x ^{5}}) d x