Final answer to the problem
$\frac{1}{2}\cdot 4^2\mathrm{arcsec}\left(4\right)- \left(\frac{1}{2}\right)\cdot 2^2\mathrm{arcsec}\left(2\right)+\frac{-\sqrt{15}+\sqrt{3}}{2}$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
We can solve the integral $\int x\mathrm{arcsec}\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
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$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve problems step by step online. Integrate the function xarcsec(x) from 2 to 4. We can solve the integral \int x\mathrm{arcsec}\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Final answer to the problem
$\frac{1}{2}\cdot 4^2\mathrm{arcsec}\left(4\right)- \left(\frac{1}{2}\right)\cdot 2^2\mathrm{arcsec}\left(2\right)+\frac{-\sqrt{15}+\sqrt{3}}{2}$
