Final answer to the problem
$\frac{6\tan\left(\frac{u}{2}\right)+2\tan\left(\frac{u}{2}\right)^{3}}{3\left(y^2+6y+1\right)}+C_0$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Solve the trigonometric integral int(1/(sin(u)^2+1))du. We can solve the integral \int\frac{1}{\sin\left(u\right)^2+1}du by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.
Final answer to the problem
$\frac{6\tan\left(\frac{u}{2}\right)+2\tan\left(\frac{u}{2}\right)^{3}}{3\left(y^2+6y+1\right)}+C_0$
