What is the integral of 3xe^{7x^2} ?

The integral of 3xe^{7x^2} is 3/14 e^{7x^2}+C

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integral of 3xe^{7x^2}

\int 3 x e^{7 x^{2}} d x

\frac{3}{14} e^{7 x^{2}} + C

Solution steps

\int 3 x e^{7 x^{2}} d x

Take the constant out:

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

= 3 \cdot \int x e^{7 x^{2}} d x

Apply u-substitution

= 3 \cdot \int \frac{e ^{u}}{14} d u

Take the constant out:

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

= 3 \cdot \frac{1}{14} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{14} e^{u}

Substitute back

u = 7 x^{2}

= 3 \cdot \frac{1}{14} e^{7 x^{2}}

Simplify

3 \cdot \frac{1}{14} e^{7 x^{2}} : \frac{3}{14} e^{7 x^{2}}

= \frac{3}{14} e^{7 x^{2}}

Add a constant to the solution

= \frac{3}{14} e^{7 x^{2}} + C

f (x) = 16 cos (2 x)

\int csc^{2} (x) d x

f (x) = tan (\frac{π x}{2})

x \to 0 lim (\frac{3 x ^{2} - 4 x}{x})

\int ln (2 x + 7) d x

What is the integral of 3xe^{7x^2} ?
The integral of 3xe^{7x^2} is 3/14 e^{7x^2}+C