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Exercise

$\int_1^x-\frac{\left(1\right)}{2+t}dt$

Step-by-step Solution

1

Apply the formula: $\int\frac{n}{x+b}dx$$=nsign\left(x\right)\ln\left(x+b\right)+C$, where $b=2$, $x=t$ and $n=-1$

$\left[-\ln\left|t+2\right|\right]_{1}^{x}$
2

Evaluate the definite integral

$-\ln\left|x+2\right|- -\ln\left|1+2\right|$

Final answer to the exercise

$-\ln\left|x+2\right|- -\ln\left|1+2\right|$

Try other ways to solve this exercise

  • Choose an option
  • 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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