Final Answer
$t\tan\left(t\right)^2+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(\frac{\sin\left(t\right)}{\cos\left(t\right)}\right)^2dt$
Specify the solving method
1
Simplify $\left(\frac{\sin\left(t\right)}{\cos\left(t\right)}\right)^2$ into $\tan\left(t\right)^2$ by applying trigonometric identities
$\int\tan\left(t\right)^2dt$
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$\int\tan\left(t\right)^2dt$
Learn how to solve problems step by step online. Solve the trigonometric integral int(((sin(t)/(cos(t))^2)dt. Simplify \left(\frac{\sin\left(t\right)}{\cos\left(t\right)}\right)^2 into \tan\left(t\right)^2 by applying trigonometric identities. The integral of a constant is equal to the constant times the integral's variable. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.
Final Answer
$t\tan\left(t\right)^2+C_0$