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Exercise

$\int sec\:\left(0.05\cdot x\right)-1$

Step-by-step Solution

1

Expand the integral $\int\left(\sec\left(0.05x\right)-1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\sec\left(0.05x\right)dx+\int-1dx$
2

The integral $\int\sec\left(0.05x\right)dx$ results in: $20\ln\left(\sec\left(0.05x\right)+\tan\left(0.05x\right)\right)$

$20\ln\left(\sec\left(0.05x\right)+\tan\left(0.05x\right)\right)$
3

The integral $\int-1dx$ results in: $-x$

$-x$
4

Gather the results of all integrals

$20\ln\left|\sec\left(0.05x\right)+\tan\left(0.05x\right)\right|-x$
5

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$20\ln\left|\sec\left(0.05x\right)+\tan\left(0.05x\right)\right|-x+C_0$

Final answer to the exercise

$20\ln\left|\sec\left(0.05x\right)+\tan\left(0.05x\right)\right|-x+C_0$

Try other ways to solve this exercise

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  • Integrate using basic integrals
  • Product of Binomials with Common Term
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