What is the integral of xe^{10x} ?

The integral of xe^{10x} is 1/100 (e^{10x}*10x-e^{10x})+C

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integral of xe^{10x}

\int x e^{10 x} d x

\frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x}) + C

Solution steps

\int x e^{10 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{100} d u

= \int \frac{e ^{u} u}{100} d u

Take the constant out:

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

= \frac{1}{100} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{100} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{100} (e^{u} u - e^{u})

Substitute back

u = 10 x

= \frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x})

Add a constant to the solution

= \frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x}) + C

x \to - b lim \frac{( ( x + b ) ^{7} + ( x + b ) ^{10} )}{4 ( x + b )}

\frac{\partial}{\partial x} ((x + y)^{2} + (x + 1)^{2})

\int \frac{1}{2} sin^{2} (x) d x

\frac{\partial}{\partial x} (x + y^{2})

\frac{3}{s ^{2} + 6 s + 10}

What is the integral of xe^{10x} ?
The integral of xe^{10x} is 1/100 (e^{10x}*10x-e^{10x})+C