What is the integral of 0.1e^{0.4x} ?

The integral of 0.1e^{0.4x} is 0.25e^{0.4x}+C

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integral of 0.1e^{0.4x}

\int 0.1 e^{0.4 x} d x

0.25 e^{0.4 x} + C

Solution steps

\int 0.1 e^{0.4 x} d x

Take the constant out:

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

= 0.1 \cdot \int e^{0.4 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{0.4} d u

= 0.1 \cdot \int e^{u} \frac{1}{0.4} d u

Take the constant out:

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

= 0.1 \cdot \frac{1}{0.4} \cdot \int e^{u} d u

Simplify

= 0.1 \cdot 2.5 \cdot \int e^{u} d u

Use the common integral:

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

= 0.1 \cdot 2.5 e^{u}

Substitute back

u = 0.4 x

= 0.1 \cdot 2.5 e^{0.4 x}

Simplify

= 0.25 e^{0.4 x}

Add a constant to the solution

= 0.25 e^{0.4 x} + C

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\int \frac{1}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\frac{d y}{d x} = (x + y - 2)^{2}

\frac{d ^{2}}{d x ^{2}} (3 x - 7)

What is the integral of 0.1e^{0.4x} ?
The integral of 0.1e^{0.4x} is 0.25e^{0.4x}+C