What is the integral of 10e^{10x} ?

The integral of 10e^{10x} is e^{10x}+C

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integral of 10e^{10x}

\int 10 e^{10 x} d x

e^{10 x} + C

Solution steps

\int 10 e^{10 x} d x

Take the constant out:

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

= 10 \cdot \int e^{10 x} d x

Apply u-substitution

= 10 \cdot \int e^{u} \frac{1}{10} d u

Take the constant out:

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

= 10 \cdot \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

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

= 10 \cdot \frac{1}{10} e^{u}

Substitute back

u = 10 x

= 10 \cdot \frac{1}{10} e^{10 x}

Simplify

10 \cdot \frac{1}{10} e^{10 x} : e^{10 x}

= e^{10 x}

Add a constant to the solution

= e^{10 x} + C