Choosing an indefinite integration rule: check 1
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=5 x^{3} + 20 x\), on real x.
Find the coefficient of x^4 in a primitive.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=2 x^{4} + 21 x\), on real x.
Find the coefficient of x^5 in a primitive.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: check 2
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=2 e^{3 x}\), on real x.
For \(G(x)=\frac{2 e^{3 x}}{3}+C\) with G(0)=21, find C.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=3 e^{x}\), on real x.
For \(G(x)=3 e^{x}+C\) with G(0)=22, find C.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: check 3
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=22 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\), on real x.
For \(G(x)=3 \sin{\left(x \right)} - 22 \cos{\left(x \right)}+C\) with G(0)=23, find C.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=23 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}\), on real x.
For \(G(x)=2 \sin{\left(2 x \right)} - \frac{23 \cos{\left(2 x \right)}}{2}+C\) with G(0)=24, find C.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: check 4
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{4}{2 x + 3}\), on \(x>- \frac{3}{2}\).
Find the x-coordinate of the pole.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Choosing an indefinite integration rule: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{5}{3 x + 4}\), on \(x>- \frac{4}{3}\).
Find the x-coordinate of the pole.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.