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

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

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integral of e^{7x}

\int e^{7 x} d x

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

Solution steps

\int e^{7 x} d x

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 x

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

Add a constant to the solution

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

y^{^{''}} + 2 y^{^{'}} + 1 y = 1, y (1) = 1, y^{^{'}} (1) = 0

n \to \infty lim (n^{2} x)

f (x) = e^{13}

y^{^{'}} - \frac{4}{x} y = \frac{y ^{4}}{x ^{4}}, y (1) = 1

\frac{\partial}{\partial x} (- x z)