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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of dx/x
- Integral of x^2/sqrt(a^2-x^2)
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Integral of sec^5(x)
- Integral of 4sinx+8x^3-11/cos^2x
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Identical expressions
- sec^ five (x)
- sec to the power of 5(x)
- sec to the power of five (x)
- sec5(x)
- sec5x
- sec⁵(x)
- sec^5x
- sec^5(x)dx
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Similar expressions
- (tan^4x/sec^5x)dx
Integral of sec^5(x) dx
The solution
You have entered
[src]
1 / | | 5 | sec (x) dx | / 0
$$\int\limits_{0}^{1} \sec^{5}{\left(x \right)}\, dx$$
Integral(sec(x)^5, (x, 0, 1))
The answer (Indefinite)
[src]
/ | 3 | 5 3*log(-1 + sin(x)) 3*log(1 + sin(x)) -5*sin(x) + 3*sin (x) | sec (x) dx = C - ------------------ + ----------------- - -------------------------- | 16 16 2 4 / 8 - 16*sin (x) + 8*sin (x)
$${{3\,\log \left(\sin x+1\right)}\over{16}}-{{3\,\log \left(\sin x-1
\right)}\over{16}}-{{3\,\sin ^3x-5\,\sin x}\over{8\,\sin ^4x-16\,
\sin ^2x+8}}$$
The graph
The answer
[src]
3
3*log(1 - sin(1)) 3*log(1 + sin(1)) -5*sin(1) + 3*sin (1)
- ----------------- + ----------------- - --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$${{3\,\log \left(\sin 1+1\right)}\over{16}}-{{3\,\log \left(1-\sin 1
\right)}\over{16}}-{{3\,\sin ^31}\over{8\,\sin ^41-16\,\sin ^21+8}}+
{{5\,\sin 1}\over{8\,\sin ^41-16\,\sin ^21+8}}$$
=
=
3
3*log(1 - sin(1)) 3*log(1 + sin(1)) -5*sin(1) + 3*sin (1)
- ----------------- + ----------------- - --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{- 5 \sin{\left(1 \right)} + 3 \sin^{3}{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8}$$
The graph
Use the examples entering the upper and lower limits of integration.