Integration by Substitution

Use the indicated substitution to evaluate the integral.

 $\int\sin\left(2x\right)\ dx,\ \ \ \ \ \ u=2x$  

•  $\cos\left(2x\right)+C$  

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

•  $-\cos\left(2x\right)+C$  

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

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 the indicated substitution to evaluate the integral.

 $\int\sec2x\ \tan2x\ dx\ ,\ \ \ u=2x$  

•  $\frac{1}{2}\sec2x+C$  

•  $-\sec2x+C$  

•  $-\frac{1}{2}\csc2x\ +C$  

•  $-\frac{1}{2}\sec2x+C$  

Use the indicated substitution to evaluate the integral.

 $\int-3\cos x\sin\left(\sin x\right)\ dx\ ,\ \ \ u=\sin x$  

•  $3\sec\left(\sin x\right)+C$  

•  $3\sin\left(\sin x\right)+C$  

•  $3\cot\left(\sin x\right)+C$  

•  $3\cos\left(\sin x\right)+C$  

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 $\int\left(3x^3+5\right)^5\cdot27x^2dx$ 

•  $\frac{1}{2}\left(3x^3+5\right)^6+C$ 

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

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

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

Use substitution to evaluate the integral $\int4\sec^24x\ \sqrt{\tan4x}\ dx$

• $2\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{15}{4}\cdot\left(\tan4x\right)^{\frac{4}{3}}+C$

• $\frac{4}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{2}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$