Section 9
Integration of Product or Composite Functions
For Activities 1 through $20,$ write the general antiderivative.1. $\int 2 e^{2 x} d x$
Write the general antiderivative.$\int 2 x e^{x^{2}} d x$
Write the general antiderivative.$\int 3 x e^{2 x^{2}} d x$
Write the general antiderivative.$\int 3(\ln 2) 2^{x}\left(1+2^{x}\right)^{3} d x$
Write the general antiderivative.$\int\left(1+e^{x}\right)^{2} e^{x} d x$
Write the general antiderivative.$\int e^{x} \sqrt{1+e^{x}} d x$
Write the general antiderivative.$\int \frac{2^{x}}{2^{x}+2} d x$
Write the general antiderivative.$\int \frac{5 e^{x}}{e^{x}+2} d x$
Write the general antiderivative.$\int \ln x d x, x>0$
Write the general antiderivative.$\int \frac{(\ln x)^{4}}{x} d x$
Write the general antiderivative.$\int \frac{\ln x}{x} d x$
Write the general antiderivative.$\int \frac{5(\ln x)^{4}}{x} d x$
Write the general antiderivative.$\int 2 x \ln \left(x^{2}+1\right) d x$
Write the general antiderivative.$\int x \ln \left(x^{2}+1\right) d x$
Write the general antiderivative.$\int \frac{2 x}{x^{2}+1} d x$
Write the general antiderivative.$\int \frac{1}{x(\ln x)^{2}} d x$
Write the general antiderivative.$\int 2 x^{2}\left(x^{3}+5\right)^{\frac{1}{4}} d x$
Write the general antiderivative.$\int \frac{x^{2}+1}{2 x} d x$
Write the general antiderivative.$\int \frac{x^{2}+1}{x^{2}} d x$
Write the general antiderivative.$\int x^{2}\left(5 x^{3}-7\right)^{4} d x$
For Activities 21 through 24a. write the general antiderivative,b. evaluate the expression.$\int_{0}^{4} 2 e^{2 x} d x$
a. write the general antiderivative,b. evaluate the expression.$\int_{2}^{8} \frac{2^{x}}{2^{x}+2} d x$
a. write the general antiderivative,b. evaluate the expression.$\int_{0}^{5}(\sin x)^{2} \cos x d x$
a. write the general antiderivative,b. evaluate the expression.$\int_{0}^{2} e^{\sin x} \cos x d x$