What is the integral of e^{7x+5} ?

The integral of e^{7x+5} is 1/7 e^{7x+5}+C

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integral of e^{7x+5}

\int e^{7 x + 5} d x

\frac{1}{7} e^{7 x + 5} + C

Solution steps

\int e^{7 x + 5} 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 + 5

= \frac{1}{7} e^{7 x + 5}

Add a constant to the solution

= \frac{1}{7} e^{7 x + 5} + C

\frac{d}{d x} (4 (5 - 9 x)^{5})

\frac{d}{d x} (tan^{l n (5 x)} (cos (x)))

arctan (e^{x})

- x^{2} + 2 x, y = x^{3} + x^{2} - 6 x

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