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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 4x²
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Integral of (x-x^2)
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Integral of 1/((x+1)(x^2+1))
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Integral of x*(x+1)^1/2
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Identical expressions
- (one /cos^2x-sinx)dx
- (1 divide by co sinus of e of squared x minus sinus of x)dx
- (one divide by co sinus of e of squared x minus sinus of x)dx
- (1/cos2x-sinx)dx
- 1/cos2x-sinxdx
- (1/cos²x-sinx)dx
- (1/cos to the power of 2x-sinx)dx
- 1/cos^2x-sinxdx
- (1 divide by cos^2x-sinx)dx
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Similar expressions
- (1/cos^2x+sinx)dx
Integral of (1/cos^2x-sinx)dx dx
The solution
You have entered
[src]
n - 4 / | | / 1 \ | |------- - sin(x)| dx | | 2 | | \cos (x) / | / -n --- 4
$$\int\limits_{- \frac{n}{4}}^{\frac{n}{4}} \left(- \sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx$$
Integral(1/(cos(x)^2) - sin(x), (x, -n/4, n/4))
Detail solution
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
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The integral of sine is negative cosine:
So, the result is:
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Don't know the steps in finding this integral.
But the integral is
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]
/ | | / 1 \ sin(x) | |------- - sin(x)| dx = C + ------ + cos(x) | | 2 | cos(x) | \cos (x) / | /
$$\int \left(- \sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx = C + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \cos{\left(x \right)}$$
The answer
[src]
/n\
2*sin|-|
\4/
--------
/n\
cos|-|
\4/
$$\frac{2 \sin{\left(\frac{n}{4} \right)}}{\cos{\left(\frac{n}{4} \right)}}$$
=
=
/n\
2*sin|-|
\4/
--------
/n\
cos|-|
\4/
$$\frac{2 \sin{\left(\frac{n}{4} \right)}}{\cos{\left(\frac{n}{4} \right)}}$$
2*sin(n/4)/cos(n/4)
Use the examples entering the upper and lower limits of integration.