Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x×e^x
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Integral of 1/(x²+1)
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Integral of f(x)=4x
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Integral of x/sin^2(x)
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Identical expressions
- 15a(tan^3at*sec^3at)*dt
- 15a( tangent of cubed at multiply by sec cubed at) multiply by dt
- 15a(tan3at*sec3at)*dt
- 15atan3at*sec3at*dt
- 15a(tan³at*sec³at)*dt
- 15a(tan to the power of 3at*sec to the power of 3at)*dt
- 15a(tan^3atsec^3at)dt
- 15a(tan3atsec3at)dt
- 15atan3atsec3atdt
- 15atan^3atsec^3atdt
Integral of 15a(tan^3at*sec^3at)*dt dx
The solution
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[src]
1 / | | 3 3 | 15*a*tan (a*t)*sec (a*t)*1 dt | / 0
$$\int\limits_{0}^{1} 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)} 1\, dt$$
Integral(15*a*tan(a*t)^3*sec(a*t)^3*1, (t, 0, 1))
The answer (Indefinite)
[src]
// 0 for a = 0\
/ || |
| || 3 5 |
| 3 3 || sec (a*t) sec (a*t) |
| 15*a*tan (a*t)*sec (a*t)*1 dt = C + 15*a*|<- --------- + --------- |
| || 3 5 |
/ ||----------------------- otherwise|
|| a |
\\ /
$$\int 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)} 1\, dt = C + 15 a \left(\begin{cases} 0 & \text{for}\: a = 0 \\\frac{\frac{\sec^{5}{\left(a t \right)}}{5} - \frac{\sec^{3}{\left(a t \right)}}{3}}{a} & \text{otherwise} \end{cases}\right)$$
The answer
[src]
/ 2 | 3 - 5*cos (a) |2 + ------------- for And(a > -oo, a < oo, a != 0) < 5 | cos (a) | \ 0 otherwise
$$\begin{cases} \frac{3 - 5 \cos^{2}{\left(a \right)}}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 2 | 3 - 5*cos (a) |2 + ------------- for And(a > -oo, a < oo, a != 0) < 5 | cos (a) | \ 0 otherwise
$$\begin{cases} \frac{3 - 5 \cos^{2}{\left(a \right)}}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.