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How to use it?
- Integral of d{x}:
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Integral of cotx
- Integral of xlnxdx
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Integral of x^(4/5)
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Integral of tan⁵x
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Identical expressions
- sqrt(six hundred and twenty-five -(x+ four)^ two)- fifteen
- square root of (625 minus (x plus 4) squared ) minus 15
- square root of (six hundred and twenty minus five minus (x plus four) to the power of two) minus fifteen
- √(625-(x+4)^2)-15
- sqrt(625-(x+4)2)-15
- sqrt625-x+42-15
- sqrt(625-(x+4)²)-15
- sqrt(625-(x+4) to the power of 2)-15
- sqrt625-x+4^2-15
- sqrt(625-(x+4)^2)-15dx
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Similar expressions
- sqrt(625+(x+4)^2)-15
- sqrt(625-(x+4)^2)+15
- sqrt(625-(x-4)^2)-15
Integral of sqrt(625-(x+4)^2)-15 dx
The solution
You have entered
[src]
4679 ---- 500 / | | / ________________ \ | | / 2 | | \\/ 625 - (x + 4) - 15/ dx | / 0
$$\int\limits_{0}^{\frac{4679}{500}} \left(\sqrt{625 - \left(x + 4\right)^{2}} - 15\right)\, dx$$
Integral(sqrt(625 - (x + 4)^2) - 15, (x, 0, 4679/500))
Detail solution
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Integrate term-by-term:
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Don't know the steps in finding this integral.
But the integral is
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The integral of a constant is the constant times the variable of integration:
The result is:
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Now simplify:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
// /4 x \ \
|| 625*I*acosh|-- + --| 3 | 2| |
|| \25 25/ I*(4 + x) 625*I*(4 + x) |(4 + x) | |
/ ||- -------------------- + ---------------------- - ---------------------- for ---------- > 1|
| || 2 _________________ _________________ 625 |
| / ________________ \ || / 2 / 2 |
| | / 2 | || 2*\/ -625 + (4 + x) 2*\/ -625 + (4 + x) |
| \\/ 625 - (x + 4) - 15/ dx = C - 15*x + |< |
| || /4 x \ |
/ || 625*asin|-- + --| 3 |
|| \25 25/ (4 + x) 625*(4 + x) |
|| ----------------- - --------------------- + --------------------- otherwise |
|| 2 ________________ ________________ |
|| / 2 / 2 |
\\ 2*\/ 625 - (4 + x) 2*\/ 625 - (4 + x) /
$$\int \left(\sqrt{625 - \left(x + 4\right)^{2}} - 15\right)\, dx = C - 15 x + \begin{cases} \frac{i \left(x + 4\right)^{3}}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{625 i \left(x + 4\right)}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{625 i \operatorname{acosh}{\left(\frac{x}{25} + \frac{4}{25} \right)}}{2} & \text{for}\: \frac{\left|{\left(x + 4\right)^{2}}\right|}{625} > 1 \\\frac{625 \operatorname{asin}{\left(\frac{x}{25} + \frac{4}{25} \right)}}{2} - \frac{\left(x + 4\right)^{3}}{2 \sqrt{625 - \left(x + 4\right)^{2}}} + \frac{625 \left(x + 4\right)}{2 \sqrt{625 - \left(x + 4\right)^{2}}} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
4679
----
500
/
|
| / 2 3 2
| | 625*I 25*I 3*I*(4 + x) I*(4 + x) *(-4 - x) 625*I*(-4 - x)*(4 + x) (4 + x)
| |- ---------------------- - ------------------------ + ---------------------- + ---------------------- - ---------------------- for -------- > 1
| | _________________ _________________ _________________ 3/2 3/2 625
| | / 2 / 2 / 2 / 2\ / 2\
| | 2*\/ -625 + (4 + x) / /4 x \ 2*\/ -625 + (4 + x) 2*\-625 + (4 + x) / 2*\-625 + (4 + x) /
| | 2* / -1 + |-- + --|
14037 | | \/ \25 25/
- ----- + | < dx
100 | | 2 4 2
| | 25 625 3*(4 + x) (4 + x) 625*(4 + x)
| | ----------------------- + --------------------- - --------------------- - --------------------- + --------------------- otherwise
| | ________________ ________________ ________________ 3/2 3/2
| | / 2 / 2 / 2 / 2\ / 2\
| | / /4 x \ 2*\/ 625 - (4 + x) 2*\/ 625 - (4 + x) 2*\625 - (4 + x) / 2*\625 - (4 + x) /
| | 2* / 1 - |-- + --|
| \ \/ \25 25/
|
/
0
$$- \frac{14037}{100} + \int\limits_{0}^{\frac{4679}{500}} \begin{cases} \frac{i \left(- x - 4\right) \left(x + 4\right)^{3}}{2 \left(\left(x + 4\right)^{2} - 625\right)^{\frac{3}{2}}} - \frac{625 i \left(- x - 4\right) \left(x + 4\right)}{2 \left(\left(x + 4\right)^{2} - 625\right)^{\frac{3}{2}}} + \frac{3 i \left(x + 4\right)^{2}}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{625 i}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{25 i}{2 \sqrt{\left(\frac{x}{25} + \frac{4}{25}\right)^{2} - 1}} & \text{for}\: \frac{\left(x + 4\right)^{2}}{625} > 1 \\- \frac{3 \left(x + 4\right)^{2}}{2 \sqrt{625 - \left(x + 4\right)^{2}}} + \frac{625}{2 \sqrt{625 - \left(x + 4\right)^{2}}} - \frac{\left(x + 4\right)^{4}}{2 \left(625 - \left(x + 4\right)^{2}\right)^{\frac{3}{2}}} + \frac{625 \left(x + 4\right)^{2}}{2 \left(625 - \left(x + 4\right)^{2}\right)^{\frac{3}{2}}} + \frac{25}{2 \sqrt{1 - \left(\frac{x}{25} + \frac{4}{25}\right)^{2}}} & \text{otherwise} \end{cases}\, dx$$
=
=
4679
----
500
/
|
| / 2 3 2
| | 625*I 25*I 3*I*(4 + x) I*(4 + x) *(-4 - x) 625*I*(-4 - x)*(4 + x) (4 + x)
| |- ---------------------- - ------------------------ + ---------------------- + ---------------------- - ---------------------- for -------- > 1
| | _________________ _________________ _________________ 3/2 3/2 625
| | / 2 / 2 / 2 / 2\ / 2\
| | 2*\/ -625 + (4 + x) / /4 x \ 2*\/ -625 + (4 + x) 2*\-625 + (4 + x) / 2*\-625 + (4 + x) /
| | 2* / -1 + |-- + --|
14037 | | \/ \25 25/
- ----- + | < dx
100 | | 2 4 2
| | 25 625 3*(4 + x) (4 + x) 625*(4 + x)
| | ----------------------- + --------------------- - --------------------- - --------------------- + --------------------- otherwise
| | ________________ ________________ ________________ 3/2 3/2
| | / 2 / 2 / 2 / 2\ / 2\
| | / /4 x \ 2*\/ 625 - (4 + x) 2*\/ 625 - (4 + x) 2*\625 - (4 + x) / 2*\625 - (4 + x) /
| | 2* / 1 - |-- + --|
| \ \/ \25 25/
|
/
0
$$- \frac{14037}{100} + \int\limits_{0}^{\frac{4679}{500}} \begin{cases} \frac{i \left(- x - 4\right) \left(x + 4\right)^{3}}{2 \left(\left(x + 4\right)^{2} - 625\right)^{\frac{3}{2}}} - \frac{625 i \left(- x - 4\right) \left(x + 4\right)}{2 \left(\left(x + 4\right)^{2} - 625\right)^{\frac{3}{2}}} + \frac{3 i \left(x + 4\right)^{2}}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{625 i}{2 \sqrt{\left(x + 4\right)^{2} - 625}} - \frac{25 i}{2 \sqrt{\left(\frac{x}{25} + \frac{4}{25}\right)^{2} - 1}} & \text{for}\: \frac{\left(x + 4\right)^{2}}{625} > 1 \\- \frac{3 \left(x + 4\right)^{2}}{2 \sqrt{625 - \left(x + 4\right)^{2}}} + \frac{625}{2 \sqrt{625 - \left(x + 4\right)^{2}}} - \frac{\left(x + 4\right)^{4}}{2 \left(625 - \left(x + 4\right)^{2}\right)^{\frac{3}{2}}} + \frac{625 \left(x + 4\right)^{2}}{2 \left(625 - \left(x + 4\right)^{2}\right)^{\frac{3}{2}}} + \frac{25}{2 \sqrt{1 - \left(\frac{x}{25} + \frac{4}{25}\right)^{2}}} & \text{otherwise} \end{cases}\, dx$$
-14037/100 + Integral(Piecewise((-625*i/(2*sqrt(-625 + (4 + x)^2)) - 25*i/(2*sqrt(-1 + (4/25 + x/25)^2)) + 3*i*(4 + x)^2/(2*sqrt(-625 + (4 + x)^2)) + i*(4 + x)^3*(-4 - x)/(2*(-625 + (4 + x)^2)^(3/2)) - 625*i*(-4 - x)*(4 + x)/(2*(-625 + (4 + x)^2)^(3/2)), (4 + x)^2/625 > 1), (25/(2*sqrt(1 - (4/25 + x/25)^2)) + 625/(2*sqrt(625 - (4 + x)^2)) - 3*(4 + x)^2/(2*sqrt(625 - (4 + x)^2)) - (4 + x)^4/(2*(625 - (4 + x)^2)^(3/2)) + 625*(4 + x)^2/(2*(625 - (4 + x)^2)^(3/2)), True)), (x, 0, 4679/500))
Use the examples entering the upper and lower limits of integration.