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How to use it?
- Integral of d{x}:
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Integral of x^(-1/2)
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Integral of sin²xcos²x
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Integral of x*2^(-x)
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Integral of y^(-2/3)
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Identical expressions
- (sqrt(x))((ln(x))/(ln(two)))
- ( square root of (x))((ln(x)) divide by (ln(2)))
- ( square root of (x))((ln(x)) divide by (ln(two)))
- (√(x))((ln(x))/(ln(2)))
- sqrtxlnx/ln2
- (sqrt(x))((ln(x)) divide by (ln(2)))
- (sqrt(x))((ln(x))/(ln(2)))dx
Integral of (sqrt(x))((ln(x))/(ln(2))) dx
The solution
You have entered
[src]
4 / | | ___ log(x) | \/ x *------ dx | log(2) | / 1
$$\int\limits_{1}^{4} \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx$$
Integral(sqrt(x)*(log(x)/log(2)), (x, 1, 4))
The answer (Indefinite)
[src]
/ 3/2 3/2 \ / | 2*x x *log(x)| | 2*|- ------ + -----------| | ___ log(x) \ 9 3 / | \/ x *------ dx = C + -------------------------- | log(2) log(2) | /
$$\int \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx = C + \frac{2 \left(\frac{x^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{2 x^{\frac{3}{2}}}{9}\right)}{\log{\left(2 \right)}}$$
The answer
[src]
32 16*log(4)
- -- + ---------
4 9 3
-------- + ----------------
9*log(2) log(2)
$$\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}}$$
=
=
32 16*log(4)
- -- + ---------
4 9 3
-------- + ----------------
9*log(2) log(2)
$$\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}}$$
4/(9*log(2)) + (-32/9 + 16*log(4)/3)/log(2)
Use the examples entering the upper and lower limits of integration.