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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of sin(w*t)^2
- Integral of sin(log(x))^2/x
- Integral of sin^n(x)
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Identical expressions
- (x+ one)/((x+ two)sqrt(3x+ two))
- (x plus 1) divide by ((x plus 2) square root of (3x plus 2))
- (x plus one) divide by ((x plus two) square root of (3x plus two))
- (x+1)/((x+2)√(3x+2))
- x+1/x+2sqrt3x+2
- (x+1) divide by ((x+2)sqrt(3x+2))
- (x+1)/((x+2)sqrt(3x+2))dx
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Similar expressions
- (x+1)/((x+2)sqrt(3x-2))
- (x+1)/((x-2)sqrt(3x+2))
- (x-1)/((x+2)sqrt(3x+2))
Integral of (x+1)/((x+2)sqrt(3x+2)) dx
The solution
You have entered
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1 / | | x + 1 | ------------------- dx | _________ | (x + 2)*\/ 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{x + 1}{\left(x + 2\right) \sqrt{3 x + 2}}\, dx$$
Integral((x + 1)/(((x + 2)*sqrt(3*x + 2))), (x, 0, 1))
The answer (Indefinite)
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/ | / _________\ _________ | x + 1 |\/ 2 + 3*x | 2*\/ 2 + 3*x | ------------------- dx = C - atan|-----------| + ------------- | _________ \ 2 / 3 | (x + 2)*\/ 3*x + 2 | /
$$\int \frac{x + 1}{\left(x + 2\right) \sqrt{3 x + 2}}\, dx = C + \frac{2 \sqrt{3 x + 2}}{3} - \operatorname{atan}{\left(\frac{\sqrt{3 x + 2}}{2} \right)}$$
The graph
The answer
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___ ___ / ___\
/ ___\ 2*\/ 2 2*\/ 5 |2*\/ 5 |
- atan\\/ 2 / - ------- + ------- + atan|-------|
3 3 \ 5 /
$$- \operatorname{atan}{\left(\sqrt{2} \right)} - \frac{2 \sqrt{2}}{3} + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \frac{2 \sqrt{5}}{3}$$
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___ ___ / ___\
/ ___\ 2*\/ 2 2*\/ 5 |2*\/ 5 |
- atan\\/ 2 / - ------- + ------- + atan|-------|
3 3 \ 5 /
$$- \operatorname{atan}{\left(\sqrt{2} \right)} - \frac{2 \sqrt{2}}{3} + \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \frac{2 \sqrt{5}}{3}$$
-atan(sqrt(2)) - 2*sqrt(2)/3 + 2*sqrt(5)/3 + atan(2*sqrt(5)/5)
Use the examples entering the upper and lower limits of integration.