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

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

Popular >

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

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

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

Solution steps

\int e^{3 x} (x - 1) 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 )}{1 + sin ^{4} ( x )} d x

\int cos (2 x + 1) x d x

\int \frac{1}{x ^{2} + 2 x + 3} d x

\int \frac{x ^{3}}{( 1 + x ^{2} ) ^{2}} d x

\int \frac{x ^{5}}{1 + x ^{2}} d x

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