What is the integral of 56xe^{7x^2} ?

The integral of 56xe^{7x^2} is 4e^{7x^2}+C

Popular >

integral of 56xe^{7x^2}

\int 56 x e^{7 x^{2}} d x

4 e^{7 x^{2}} + C

Solution steps

\int 56 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

= 56 \cdot \int x e^{7 x^{2}} d x

Apply u-substitution

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

= 56 \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

= 56 \cdot \frac{1}{14} \cdot \int e^{u} d u

Use the common integral:

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

= 56 \cdot \frac{1}{14} e^{u}

Substitute back

u = 7 x^{2}

= 56 \cdot \frac{1}{14} e^{7 x^{2}}

Simplify

56 \cdot \frac{1}{14} e^{7 x^{2}} : 4 e^{7 x^{2}}

= 4 e^{7 x^{2}}

Add a constant to the solution

= 4 e^{7 x^{2}} + C

y^{^{'}} + 2 y^{2} cos (x + 1) = 0

\frac{d}{d x} (f (x) \cdot f (x))

x \to 4 - lim (arcsin (\frac{x}{4}))

x \to 0 lim (\frac{x ^{2} h + 3 x h ^{2} + h ^{3}}{2 x h + 5 h ^{2}})

y = x + 2, y = \frac{1}{x + 1}, x = 2, x = 0

What is the integral of 56xe^{7x^2} ?
The integral of 56xe^{7x^2} is 4e^{7x^2}+C