What is the integral of 0.5e^{0.1x} ?

The integral of 0.5e^{0.1x} is 5e^{0.1x}+C

Popular >

integral of 0.5e^{0.1x}

\int 0.5 e^{0.1 x} d x

5 e^{0.1 x} + C

Solution steps

\int 0.5 e^{0.1 x} d x

Take the constant out:

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

= 0.5 \cdot \int e^{0.1 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.1} d u

= 0.5 \cdot \int e^{u} \frac{1}{0.1} d u

Take the constant out:

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

= 0.5 \cdot \frac{1}{0.1} \cdot \int e^{u} d u

Simplify

= 0.5 \cdot 10 \cdot \int e^{u} d u

Use the common integral:

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

= 0.5 \cdot 10 e^{u}

Substitute back

u = 0.1 x

= 0.5 \cdot 10 e^{0.1 x}

Simplify

= 5 e^{0.1 x}

Add a constant to the solution

= 5 e^{0.1 x} + C

\int tan (1 + π t - t) d t

\int \frac{10 x ^{3}}{x ^{2} + 9} d x

\int - 11

\int \frac{x ^{2}}{64 + x ^{2}} d x

\int (cos (θ) + sin (θ)) d θ

What is the integral of 0.5e^{0.1x} ?
The integral of 0.5e^{0.1x} is 5e^{0.1x}+C