What is the integral of x^2*3^x ?

The integral of x^2*3^x is (3^xx^2)/(ln(3))-2/(ln(3))((3^xx)/(ln(3))-(3^x)/(ln^2(3)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2*3^x

\int x^{2} \cdot 3^{x} d x

\frac{3 ^{x} x ^{2}}{ln ( 3 )} - \frac{2}{ln ( 3 )} (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )}) + C

Solution steps

\int x^{2} \cdot 3^{x} d x

Apply Integration By Parts

: \frac{3 ^{x} x ^{2}}{ln ( 3 )} - \int \frac{2 \cdot 3 ^{x} x}{ln ( 3 )} d x

= \frac{3 ^{x} x ^{2}}{ln ( 3 )} - \int \frac{2 \cdot 3 ^{x} x}{ln ( 3 )} d x

\int \frac{2 \cdot 3 ^{x} x}{ln ( 3 )} d x = \frac{2}{ln ( 3 )} (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )})

= \frac{3 ^{x} x ^{2}}{ln ( 3 )} - \frac{2}{ln ( 3 )} (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )})

Add a constant to the solution

= \frac{3 ^{x} x ^{2}}{ln ( 3 )} - \frac{2}{ln ( 3 )} (\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )}) + C

\int 7 e^{x} + 6 sec^{2} (x) d x

\int 5 e^{\frac{x}{100}} d x

\int \frac{1}{( 2 x + 7 ) ^{3}} d x

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

\int t + sin (t) - e^{- 2 t} d t

What is the integral of x^2*3^x ?
The integral of x^2*3^x is (3^xx^2)/(ln(3))-2/(ln(3))((3^xx)/(ln(3))-(3^x)/(ln^2(3)))+C