Integral of x*2^(3x-1) dx
The solution
Detail solution
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Rewrite the integrand:
23x−1x=223xx
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The integral of a constant times a function is the constant times the integral of the function:
∫223xxdx=2∫23xxdx
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Don't know the steps in finding this integral.
But the integral is
9log(2)223x(3xlog(2)−1)
So, the result is: 18log(2)223x(3xlog(2)−1)
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Now simplify:
18log(2)223x(xlog(8)−1)
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Add the constant of integration:
18log(2)223x(xlog(8)−1)+constant
The answer is:
18log(2)223x(xlog(8)−1)+constant
The answer (Indefinite)
[src]
/
| 3*x
| 3*x - 1 2 *(-1 + 3*x*log(2))
| x*2 dx = C + ----------------------
| 2
/ 18*log (2)
18(log2)2(3log2x−1)e3log2x
The graph
1 4*(-1 + 3*log(2))
---------- + -----------------
2 2
18*log (2) 9*log (2)
9(log2)212log2−4+18(log2)21
=
1 4*(-1 + 3*log(2))
---------- + -----------------
2 2
18*log (2) 9*log (2)
18log(2)21+9log(2)24(−1+3log(2))
Use the examples entering the upper and lower limits of integration.