What is the integral of e^{7x+6} ?

The integral of e^{7x+6} is 1/7 e^{7x+6}+C

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integral of e^{7x+6}

\int e^{7 x + 6} d x

\frac{1}{7} e^{7 x + 6} + C

Solution steps

\int e^{7 x + 6} 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 + 6

= \frac{1}{7} e^{7 x + 6}

Add a constant to the solution

= \frac{1}{7} e^{7 x + 6} + C

7 x + 11 (2.5)

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x \to \frac{π}{2} lim (\frac{x}{2})

y = tan^{2} (x), (- \frac{π}{4}, 1)

\frac{\partial}{\partial y} (\frac{8 x}{y})