What is the integral of 3e^{7x} ?

The integral of 3e^{7x} is 3/7 e^{7x}+C

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integral of 3e^{7x}

\int 3 e^{7 x} d x

\frac{3}{7} e^{7 x} + C

Solution steps

\int 3 e^{7 x} d x

Take the constant out:

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

= 3 \cdot \int e^{7 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{7} d u

= 3 \cdot \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

= 3 \cdot \frac{1}{7} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{7} e^{u}

Substitute back

u = 7 x

= 3 \cdot \frac{1}{7} e^{7 x}

Simplify

3 \cdot \frac{1}{7} e^{7 x} : \frac{3}{7} e^{7 x}

= \frac{3}{7} e^{7 x}

Add a constant to the solution

= \frac{3}{7} e^{7 x} + C

y^{^{'}} = x^{2} + 2 y

\int \frac{1 - tanh ^{3} ( 3 x )}{tanh ( 3 x )} d x

\int \frac{4 x ^{3}}{3} d x

0.5 y^{^{''}} + 10 y^{^{'}} + 100 y = 150

x \to 1 lim ((x)^{\frac{1}{1 - x}})