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

The integral of e^{7x}(7) is e^{7x}+C

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integral of e^{7x}(7)

\int e^{7 x} (7) d x

e^{7 x} + C

Solution steps

\int e^{7 x} \cdot 7 d x

Take the constant out:

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

= 7 \cdot \int e^{7 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{7} d u

= 7 \cdot \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

= 7 \cdot \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= 7 \cdot \frac{1}{7} e^{u}

Substitute back

u = 7 x

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

Simplify

7 \cdot \frac{1}{7} e^{7 x} : e^{7 x}

= e^{7 x}

Add a constant to the solution

= e^{7 x} + C

x + y = 7, x + 5 = y^{2}

x = y^{2} + 2, x = 6

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