Mister Exam
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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of sin²xcos²x
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Integral of 1/(x(x+2))
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Integral of (1+2x^2)/(x^2(1+x^2))
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Integral of -15x^2
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Identical expressions
- sqrt(sqrt(x)+ three)
- square root of ( square root of (x) plus 3)
- square root of ( square root of (x) plus three)
- √(√(x)+3)
- sqrtsqrtx+3
- sqrt(sqrt(x)+3)dx
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Similar expressions
- sqrt(sqrt(x)-3)
Integral of sqrt(sqrt(x)+3) dx
The solution
You have entered
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1 / | | ___________ | / ___ | \/ \/ x + 3 dx | / 0
$$\int\limits_{0}^{1} \sqrt{\sqrt{x} + 3}\, dx$$
Integral(sqrt(sqrt(x) + 3), (x, 0, 1))
The answer (Indefinite)
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/ | ___________ ___________ ___________ ___________ | ___________ 5/2 2 ___ 2 / ___ ___ 5/2 / ___ ___ 7/2 / ___ ___ 3 / ___ | / ___ 72*x 216*x 72*\/ 3 *x *\/ 3 + \/ x 12*\/ 3 *x *\/ 3 + \/ x 4*\/ 3 *x *\/ 3 + \/ x 16*\/ 3 *x *\/ 3 + \/ x | \/ \/ x + 3 dx = C + -------------------------- + -------------------------- - -------------------------- - ---------------------------- + --------------------------- + -------------------------- | ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 / 5*\/ 3 *x + 15*\/ 3 *x 5*\/ 3 *x + 15*\/ 3 *x 5*\/ 3 *x + 15*\/ 3 *x 5*\/ 3 *x + 15*\/ 3 *x 5*\/ 3 *x + 15*\/ 3 *x 5*\/ 3 *x + 15*\/ 3 *x
$$\int \sqrt{\sqrt{x} + 3}\, dx = C + \frac{4 \sqrt{3} x^{\frac{7}{2}} \sqrt{\sqrt{x} + 3}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}} - \frac{12 \sqrt{3} x^{\frac{5}{2}} \sqrt{\sqrt{x} + 3}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}} + \frac{72 x^{\frac{5}{2}}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}} + \frac{16 \sqrt{3} x^{3} \sqrt{\sqrt{x} + 3}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}} - \frac{72 \sqrt{3} x^{2} \sqrt{\sqrt{x} + 3}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}} + \frac{216 x^{2}}{5 \sqrt{3} x^{\frac{5}{2}} + 15 \sqrt{3} x^{2}}$$
The graph
The answer
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___ 32 24*\/ 3 - -- + -------- 5 5
$$- \frac{32}{5} + \frac{24 \sqrt{3}}{5}$$
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___ 32 24*\/ 3 - -- + -------- 5 5
$$- \frac{32}{5} + \frac{24 \sqrt{3}}{5}$$
-32/5 + 24*sqrt(3)/5
Use the examples entering the upper and lower limits of integration.