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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x*2^(-x)
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Integral of ex^2
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Integral of (1/x^2)dx
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Integral of x*cos(x/2)
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Identical expressions
- (x+ four)/(sqrt(x+ one)+ seven)
- (x plus 4) divide by ( square root of (x plus 1) plus 7)
- (x plus four) divide by ( square root of (x plus one) plus seven)
- (x+4)/(√(x+1)+7)
- x+4/sqrtx+1+7
- (x+4) divide by (sqrt(x+1)+7)
- (x+4)/(sqrt(x+1)+7)dx
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Similar expressions
- (x-4)/(sqrt(x+1)+7)
- (x+4)/(sqrt(x-1)+7)
- (x+4)/(sqrt(x+1)-7)
Integral of (x+4)/(sqrt(x+1)+7) dx
The solution
You have entered
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1 / | | x + 4 | ------------- dx | _______ | \/ x + 1 + 7 | / 0
$$\int\limits_{0}^{1} \frac{x + 4}{\sqrt{x + 1} + 7}\, dx$$
Integral((x + 4)/(sqrt(x + 1) + 7), (x, 0, 1))
The answer (Indefinite)
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/ | 3/2 | x + 4 / _______\ _______ 2*(x + 1) | ------------- dx = -7 + C - 728*log\7 + \/ x + 1 / - 7*x + 104*\/ x + 1 + ------------ | _______ 3 | \/ x + 1 + 7 | /
$$\int \frac{x + 4}{\sqrt{x + 1} + 7}\, dx = C - 7 x + \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3} + 104 \sqrt{x + 1} - 728 \log{\left(\sqrt{x + 1} + 7 \right)} - 7$$
The graph
The answer
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___ 335 / ___\ 316*\/ 2 - --- - 728*log\7 + \/ 2 / + 728*log(8) + --------- 3 3
$$- 728 \log{\left(\sqrt{2} + 7 \right)} - \frac{335}{3} + \frac{316 \sqrt{2}}{3} + 728 \log{\left(8 \right)}$$
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___ 335 / ___\ 316*\/ 2 - --- - 728*log\7 + \/ 2 / + 728*log(8) + --------- 3 3
$$- 728 \log{\left(\sqrt{2} + 7 \right)} - \frac{335}{3} + \frac{316 \sqrt{2}}{3} + 728 \log{\left(8 \right)}$$
-335/3 - 728*log(7 + sqrt(2)) + 728*log(8) + 316*sqrt(2)/3
Use the examples entering the upper and lower limits of integration.