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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(e^(2*x))
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Integral of 1/(1+x^(1/2))
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Integral of (xe^x)dx
- Integral of x*cos^2(x)/(sqrt(x^6-1))
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Identical expressions
- sec^ three (pix)
- sec cubed ( Pi x)
- sec to the power of three ( Pi x)
- sec3(pix)
- sec3pix
- sec³(pix)
- sec to the power of 3(pix)
- sec^3pix
- sec^3(pix)dx
Integral of sec^3(pix) dx
The solution
You have entered
[src]
1 / | | 3 | sec (pi*x) dx | / 0
$$\int\limits_{0}^{1} \sec^{3}{\left(\pi x \right)}\, dx$$
Integral(sec(pi*x)^3, (x, 0, 1))
The answer (Indefinite)
[src]
log(-1 + sin(pi*x)) log(1 + sin(pi*x)) sin(pi*x) / - ------------------- + ------------------ - ----------------- | 4 4 2 | 3 -2 + 2*sin (pi*x) | sec (pi*x) dx = C + -------------------------------------------------------------- | pi /
$$\int \sec^{3}{\left(\pi x \right)}\, dx = C + \frac{- \frac{\log{\left(\sin{\left(\pi x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(\pi x \right)} + 1 \right)}}{4} - \frac{\sin{\left(\pi x \right)}}{2 \sin^{2}{\left(\pi x \right)} - 2}}{\pi}$$
The graph
Use the examples entering the upper and lower limits of integration.