What is the integral of (x+1)e^{7x^2+14x} ?

The integral of (x+1)e^{7x^2+14x} is 1/14 e^{7x^2+14x}+C

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integral of (x+1)e^{7x^2+14x}

\int (x + 1) e^{7 x^{2} + 14 x} d x

\frac{1}{14} e^{7 x^{2} + 14 x} + C

Solution steps

\int (x + 1) e^{7 x^{2} + 14 x} d x

Apply u-substitution

: \int \frac{e ^{u}}{14} d u

= \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

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

Use the common integral:

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

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

Substitute back

u = 7 x^{2} + 14 x

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

Add a constant to the solution

= \frac{1}{14} e^{7 x^{2} + 14 x} + C

y = \frac{x}{16 x + x ^{2}}

\int x^{16} e^{x^{17}} d x

\frac{\partial}{\partial x} (e^{7 x})

x \to 3 - lim (\frac{2}{x + 3})

\frac{d}{d x} (e^{s i n (2 x)})

What is the integral of (x+1)e^{7x^2+14x} ?
The integral of (x+1)e^{7x^2+14x} is 1/14 e^{7x^2+14x}+C