Question

solve the integral. (or find y)
y'=sin2x/(1+cos^2x)

Answer 1

Is this algebra 2A?

Answer 2

no its lvl 2 Calculus.

Answer 3

\[\int\frac{\sin2x}{1+\cos^2x}~dx~~?\]

Answer 4

\(\sin2x=2\sin x\cos x\), so you have
\[2\int\frac{\sin x\cos x}{1+\cos^2x}~dx\]
Substitute \(u=\cos x\), so that \(-du=\sin x~dx\):
\[-2\int\frac{u}{1+u^2}~du\]
Make another substitution: \(t=1+u^2\), so \(\dfrac{1}{2}dt=u~du\):
\[-\int\frac{dt}{t}\]

Answer 5

ty

Answer 6

yw