What is the integral of e^{12x} ?

The integral of e^{12x} is 1/12 e^{12x}+C

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integral of e^{12x}

\int e^{12 x} d x

\frac{1}{12} e^{12 x} + C

Solution steps

\int e^{12 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{12} d u

= \int e^{u} \frac{1}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{12} e^{u}

Substitute back

u = 12 x

= \frac{1}{12} e^{12 x}

Add a constant to the solution

= \frac{1}{12} e^{12 x} + C

π t

\frac{d}{d x} (\frac{125}{x})

\int cot^{2} (y) d y

\int e^{t} t^{2} d t

\frac{d}{d x} (cos (e^{x^{3} s i n (x)}))