Final Answer
Step-by-step Solution
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We could not solve this problem by using the method: Integration by Parts
Expand the fraction $\frac{\sin\left(x\right)+\cos\left(x\right)}{\cos\left(x\right)}$ into $2$ simpler fractions with common denominator $\cos\left(x\right)$
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$\int\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}+\frac{\cos\left(x\right)}{\cos\left(x\right)}\right)dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)+cos(x))/cos(x))dx. Expand the fraction \frac{\sin\left(x\right)+\cos\left(x\right)}{\cos\left(x\right)} into 2 simpler fractions with common denominator \cos\left(x\right). Simplify the resulting fractions. Expand the integral \int\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{\sin\left(x\right)}{\cos\left(x\right)}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \cos\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.