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Solving integrals/ t^2ln(x)dt

Integral of t^2ln(x)dt dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01t2log⁡(x) dt\int\limits_{0}^{1} t^{2} \log{\left(x \right)}\, dt 
Integral(t^2*log(x), (t, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫t2log⁡(x) dt=log⁡(x)∫t2 dt\int t^{2} \log{\left(x \right)}\, dt = \log{\left(x \right)} \int t^{2}\, dt

    1. The integral of tnt^{n} is tn+1n+1\frac{t^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫t2 dt=t33\int t^{2}\, dt = \frac{t^{3}}{3}

    So, the result is: t3log⁡(x)3\frac{t^{3} \log{\left(x \right)}}{3}

  2. Add the constant of integration:

    t3log⁡(x)3+constant\frac{t^{3} \log{\left(x \right)}}{3}+ \mathrm{constant}

The answer is:

t3log⁡(x)3+constant\frac{t^{3} \log{\left(x \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫t2log⁡(x) dt=C+t3log⁡(x)3\int t^{2} \log{\left(x \right)}\, dt = C + \frac{t^{3} \log{\left(x \right)}}{3}
Simplify
The answer [src] 
log(x)
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  3
log⁡(x)3\frac{\log{\left(x \right)}}{3} 
=
= 
log(x)
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  3
log⁡(x)3\frac{\log{\left(x \right)}}{3} 
log(x)/3

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

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