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

x \to 0 + lim (2 x)

f (x) = x + x, (49, 56)

y = x

\int 1 + x + 5 x^{2} d x

f (x) = \frac{1 - x e ^{x}}{x + e ^{x}}