What is the integral of e^{7t} ?

The integral of e^{7t} is 1/7 e^{7t}+C

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integral of e^{7t}

\int e^{7 t} d t

\frac{1}{7} e^{7 t} + C

Solution steps

\int e^{7 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{7} d u

= \int e^{u} \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{7} e^{u}

Substitute back

u = 7 t

= \frac{1}{7} e^{7 t}

Add a constant to the solution

= \frac{1}{7} e^{7 t} + C

y = 5 + 5 x^{2} - 2 x^{3}, (2, 9)

\frac{d y}{d x} = y - y^{3}

(0, - 2), (- 2, - 2)

x \to 0 lim (2 cos (2 x))

x \to 4 - lim (\frac{6}{x - 4})