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Exercise

$\int_{\sqrt{x}}^{x^4}tan\:t\:dt$

Step-by-step Solution

1

The integral of the tangent function is given by the following formula, $\displaystyle\int\tan(x)dx=-\ln(\cos(x))$

$\left[-\ln\left|\cos\left(t\right)\right|\right]_{\sqrt{x}}^{x^4}$
2

Evaluate the definite integral

$-\ln\left|\cos\left(x^4\right)\right|- -\ln\left|\cos\left(\sqrt{x}\right)\right|$

Final answer to the exercise

$-\ln\left|\cos\left(x^4\right)\right|- -\ln\left|\cos\left(\sqrt{x}\right)\right|$

Try other ways to solve this exercise

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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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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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