What is the integral of (x-1)e^{3x} ?

The integral of (x-1)e^{3x} is 1/3 e^{3x}x-4/9 e^{3x}+C

Popular >

integral of (x-1)e^{3x}

\int (x - 1) e^{3 x} d x

\frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x} + C

Solution steps

\int (x - 1) e^{3 x} d x

Apply Integration By Parts

: \frac{1}{3} e^{3 x} (x - 1) - \int \frac{1}{3} e^{3 x} d x

= \frac{1}{3} e^{3 x} (x - 1) - \int \frac{1}{3} e^{3 x} d x

\int \frac{1}{3} e^{3 x} d x = \frac{1}{9} e^{3 x}

= \frac{1}{3} e^{3 x} (x - 1) - \frac{1}{9} e^{3 x}

Simplify

\frac{1}{3} e^{3 x} (x - 1) - \frac{1}{9} e^{3 x} : \frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x}

= \frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x}

Add a constant to the solution

= \frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x} + C

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

\int \frac{1}{1 - \frac{( x ^{2} )}{64}} d x

\int \frac{- x + 2}{x} d x

\int x^{2} 1 + y^{4} d x

\int e^{x} (e^{x} + 1)^{3} d x

What is the integral of (x-1)e^{3x} ?
The integral of (x-1)e^{3x} is 1/3 e^{3x}x-4/9 e^{3x}+C