13. Integration
Standard Level
13.08 Integration using substitution
Interactive practice questions
We want to find $\int5\left(5x+4\right)^3dx$∫5(5x+4)3dx using the substitution $u=5x+4$u=5x+4.
a
Find $\frac{du}{dx}$dudx.
b
Which of the following is a correct expression relating $du$du and $dx$dx?
$du=\frac{dx}{5}$du=dx5
A
$du=dx$du=dx
B
$dx=\frac{du}{5}$dx=du5
C
c
Evaluate the integral $\int5\left(5x+4\right)^3dx$∫5(5x+4)3dx by making the substitutions from previous parts. Use $C$C as the constant term, leave your answer in terms of $x$x.
Medium
2min
We want to find $\int2x\left(x^2-5\right)^7dx$∫2x(x2−5)7dx using the substitution $u=x^2-5$u=x2−5.
Medium
2min
We want to find $\int3x^2\left(x^3+7\right)^4dx$∫3x2(x3+7)4dx using the substitution $u=x^3+7$u=x3+7.
Medium
2min
We want to find $\int\frac{6x}{\left(3x^2+2\right)^2}dx$∫6x(3x2+2)2dx using the substitution $u=3x^2+2$u=3x2+2.
Medium
2min
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