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

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

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integral of e^{6x+7}

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

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

Solution steps

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

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 x + 7

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

Add a constant to the solution

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

\frac{3}{1 + x ^{2}}

x y - π cos (y) = 3 π, (2, π)

\frac{\partial}{\partial t} (\frac{2 r + s}{t})

\frac{d}{d x} (- 12 sin (6 x))

y = (3 x + 4)^{2}