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

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

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integral of e^{ax+7}

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{a} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = a x + 7

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

Add a constant to the solution

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

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

f (x) = x^{4} - 17 x^{2} + 16, at x = 1

sin^{2} (x), sin^{3} (x), [0, π]

y = 2 x^{3}, x = 0, x = 2

y = x^{3} - 13 x^{2} + 36 x, y = - x^{3} + 13 x^{2} - 36 x