Mister Exam

Other calculators

x*3^x
Solving integrals/ x*3^x

Integral of x*3^x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     x   
 |  x*3  dx
 |         
/          
0
$$\int\limits_{0}^{1} 3^{x} x\, dx$$ 
Integral(x*3^x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                
 |                x                
 |    x          3 *(-1 + x*log(3))
 | x*3  dx = C + ------------------
 |                       2         
/                     log (3)
$$\int 3^{x} x\, dx = \frac{3^{x} \left(x \log{\left(3 \right)} - 1\right)}{\log{\left(3 \right)}^{2}} + C$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   1      3*(-1 + log(3))
------- + ---------------
   2             2       
log (3)       log (3)
$$\frac{3 \left(-1 + \log{\left(3 \right)}\right)}{\log{\left(3 \right)}^{2}} + \frac{1}{\log{\left(3 \right)}^{2}}$$ 
=
= 
   1      3*(-1 + log(3))
------- + ---------------
   2             2       
log (3)       log (3)
$$\frac{3 \left(-1 + \log{\left(3 \right)}\right)}{\log{\left(3 \right)}^{2}} + \frac{1}{\log{\left(3 \right)}^{2}}$$ 
log(3)^(-2) + 3*(-1 + log(3))/log(3)^2
Numerical answer [src] 
1.07364678050007
1.07364678050007
The graph
Integral of x*3^x dx

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator