What is the integral of 70xe^{7x^2} ?

The integral of 70xe^{7x^2} is 5e^{7x^2}+C

Popular >

integral of 70xe^{7x^2}

\int 70 x e^{7 x^{2}} d x

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

Solution steps

\int 70 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

= 70 \cdot \int x e^{7 x^{2}} d x

Apply u-substitution

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

= 70 \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

= 70 \cdot \frac{1}{14} \cdot \int e^{u} d u

Use the common integral:

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

= 70 \cdot \frac{1}{14} e^{u}

Substitute back

u = 7 x^{2}

= 70 \cdot \frac{1}{14} e^{7 x^{2}}

Simplify

70 \cdot \frac{1}{14} e^{7 x^{2}} : 5 e^{7 x^{2}}

= 5 e^{7 x^{2}}

Add a constant to the solution

= 5 e^{7 x^{2}} + C

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

sec (3 x)

\frac{x ^{2} + 1}{x + 4}

\frac{1}{6 s}

\int \frac{1}{θ ^{2}} cos (\frac{1}{θ}) d θ

What is the integral of 70xe^{7x^2} ?
The integral of 70xe^{7x^2} is 5e^{7x^2}+C