What is the integral of e^{6t} ?

The integral of e^{6t} is 1/6 e^{6t}+C

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integral of e^{6t}

\int e^{6 t} d t

\frac{1}{6} e^{6 t} + C

Solution steps

\int e^{6 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{6} d u

= \int e^{u} \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{6} e^{u}

Substitute back

u = 6 t

= \frac{1}{6} e^{6 t}

Add a constant to the solution

= \frac{1}{6} e^{6 t} + C

f (x) = \frac{A}{x ^{10}} + B e^{x}

y^{^{'}} - 5 y = 6 e^{5 x}, y (0) = 0

\frac{d}{d x} (ln (2 x^{2} - 3 x + 1))

y = x^{2} + 5 x + 6

f (x) = x x, at x = 9