谁的导数是1⼀(√(1 +x눀)),谢谢啦

2025-03-04 08:12:08
推荐回答(1个)
回答1:

y'=1/(√(1 +x²))
y=∫dx/(√(1 +x²),设x=tant,则:
y=∫dtant/(√(1 +tan²t)
=∫sec^2dt/sect
=∫sectdt
=∫dt/cost
=∫dsint/(1-sin^2 t)
=(1/2)[∫d(1+sint)/(1+sint)-∫d(1-sint)/(1-sint)]
=(1/2)ln(1+sint)/(1-sint)+c
=ln(x+√(1+x^2))+c.