INTEGRATION BY ALGEBRAIC SUBSTITUTION

 $\int_{ }^{ }\left(1-3x\right)^{\frac{1}{3}}dx$  

•  $-\frac{\left(1-4x\right)^{\frac{3}{4}}}{3}+C$  

•  $-\frac{\left(1-4x\right)^{\frac{4}{3}}}{4}+C$  

•  $\frac{\left(1-4x\right)^{\frac{4}{3}}}{3}+C$  

• none of the above

Use the indicated substitution to evaluate the integral.

 $\int2x\cos(x^2)\ dx\ ,\ \ \ \ u=x^2$  

•  $\sin\left(x^2\right)+C$  

•  $2\sin\left(x^2\right)+C$  

•  $\frac{1}{2}\sin\left(x^2\right)+C$  

•  $4\cos\left(x^2\right)+C$  

Use the indicated substitution to evaluate the integral.

 $\int x\left(x^2+5\right)^7dx\ ,\ \ \ \ u\ =\ x^2+5$  

•  $\frac{\left(2x+5\right)^8}{8}+c$  

•  $\frac{\left(x^2+5\right)^8}{16}+c$  

•  $\frac{\left(x^2+5\right)^6}{6}+c$  

•  $\frac{\left(2x+5\right)^8}{16}+c$  

Use the indicated substitution to evaluate the integral.

 $\int7x^6\left(x^7+1\right)^8dx\ ,\ \ \ u\ =\ x^7+1$  

•  $\frac{\left(x^7-1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^9}{9}+c$  

•  $\frac{\left(x^7+1\right)^8}{8}+c$  

•  $\frac{\left(7x^6+1\right)^9}{9}+c$  

Use the indicated substitution to evaluate the integral.

 $\int\frac{2x}{\sqrt{3+x^2}}dx\ ,\ \ \ u=3+x^2$  

•  $\frac{1}{2\sqrt{3+x^2}}+C$  

•  $\sqrt{3+x^2}+C$  

•  $2\sqrt{3+x^2}+C$  

•  $\frac{2}{\sqrt{3+x^3}}+C$  

Use substitution to evaluate the integral $\int\frac{2x}{\left(x^2+3\right)^3}\ dx$  

•  $-\frac{1}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{3}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{5}{2\left(x^2+3\right)^2}+C$  

•  $-\frac{1}{\left(x^2+3\right)^4}+C$  

Use substitution to evaluate the integral

 $\int\ x^2\sqrt{5+2x^3}\ dx$  

•  $\frac{1}{9}\left(5+2x^3\right)^{\frac{3}{2}}+C$  

•  $\frac{2}{3}\left(5+2x^3\right)^{\frac{3}{2}}+C$  

•  $6x\left(5+2x^3\right)^{\frac{3}{2}}+C$  

•  $\frac{1}{9}x^3\left(5+2x^3\right)^{\frac{3}{2}}+C$  

 $\int12x^2\left(4x^3-3\right)^5dx$  

•  $\left(4x^3-3\right)^6+C$  

•  $\frac{1}{6}\left(4x^3-3\right)^6+C$  

•  $6\left(4x^3-3\right)^6+C$  

•  $4x^3\left(x^4-3x\right)^5+C$  

Integrate  $\int\left(2x+1\right)^{10}\ dx$  with respect to x.

•  $22\left(2x+1\right)^{11}+c$  

•  $\frac{1}{22}\left(2x+1\right)^{11}+c$  

•  $11\left(2x+1\right)^{10}+c$  

•  $\frac{1}{11}\left(2x+1\right)^{10}+c$  

Which is the integral of  $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$  ?

•  $3\left(5-3x\right)^2\ +c$  

•  $\frac{\left(5-3x\right)^4}{4}+\ c$  

•  $\frac{\left(5-3x\right)^4}{12}+\ c$  

•  $-\frac{\left(5-3x\right)^4}{12}+\ c$