Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 335
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int \ln (\cos x) \tan x d x$$
Problem 336
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int x e^{-x^{2}} d x$$
Problem 337
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int x^{2} e^{-x^{3}} d x$$
Problem 338
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int e^{\sin x} \cos x d x$$
Problem 339
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int e^{\tan x} \sec ^{2} x d x$$
Problem 340
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int e^{\ln x} \frac{d x}{x}$$
Problem 341
In the following exercises, find each indefinite integral by using appropriate substitutions. $$\int \frac{e^{\ln (1-t)}}{1-t} d t$$
Problem 342
In the following exercises, verify by differentiation that \(\int \ln x d x=x(\ln x-1)+C, \quad\) then use appropriate changes of variables to compute the integral. $$\int \ln x d x \text { (Hint: } \int \ln x d x=\frac{1}{2} \int x \ln \left(x^{2}\right) d x )$$
Problem 343
In the following exercises, verify by differentiation that \(\int \ln x d x=x(\ln x-1)+C, \quad\) then use appropriate changes of variables to compute the integral. \(\int x^{2} \ln ^{2} x d x\)
Problem 344
In the following exercises, verify by differentiation that \(\int \ln x d x=x(\ln x-1)+C, \quad\) then use appropriate changes of variables to compute the integral. $$\int \frac{\ln x}{x^{2}} d x \quad\left(\text {Hint} : \text { Set } u=\frac{1}{x} .\right)$$
