·用matlab编写一个文件,实现求函数x*log(1+sqrt(1+x^2))/sqrt(1+x^2)的不定积分和导数?咋编?

Question

·用matlab编写一个文件,实现求函数x*log(1+sqrt(1+x^2))/sqrt(1+x^2)的不定积分和导数?咋编?

Answer 1

>> f=x*log(1+sqrt(1+x^2))/sqrt(1+x^2);
>> int(f)
ans =
(1+(1+x^2)^(1/2))*log(1+(1+x^2)^(1/2))-1-(1+x^2)^(1/2)
>> diff(f)
ans =
log(1+(1+x^2)^(1/2))/(1+x^2)^(1/2)+x^2/(1+x^2)/(1+(1+x^2)^(1/2))-x^2*log(1+(1+x^2)^(1/2))/(1+x^2)^(3/2)
第一个是不定积分,第二个是求导.