Integration Methods I
The best method to evaluate ∫ 3x² cos(x³) dx.
What is u-substitution?
The formula used for integration by parts.
What is ∫ u dv = uv − ∫ v du?
The best method for ∫ 1/((x+1)(x−2)) dx.
What is partial fractions?
The best method for ∫ sin³(x)cos²(x) dx.
What is trig integrals?
The best method for ∫ 1/√(x² + 9) dx.
What is trig substitution?
For √(x² + 9), the correct substitution for x is this.
What is x = 3tan(θ)?
In ∫ sin³(x)cos²(x) dx, we rewrite sin²(x) using this identity.
What is 1 − cos²(x)?
The best method to evaluate x²/((x−1)(x²+4)).
What is partial fractions?
According to LIPET, this function should be chosen as u in ∫ x ln(x) dx.
What is ln(x)?
In ∫ x e^(x²) dx, the correct substitution is this.
What is u = x²?
For ∫ x²√(x³ + 1) dx, u equals this expression.
What is x³ + 1?
In ∫ x cos(5x) dx, dv is this expression.
What is cos(5x) dx?
The decomposition form of 1/((x+1)(x−2)).
What is A/(x+1) + B/(x−2)?
∫ sin(x)cos³(x) dx evaluates to this.
What is −(1/4)cos⁴(x) + C?
For √(4 − x²), the correct substitution is this.
What is x = 2sin(θ)?
For the integral ∫ x e^(x) dx, dv is this.
What is e^(x) dx?
For∫ x cos(5x) dx, dv is this.
cos(5x)dx
The correct decomposition form for (6−2x)/(x(x+1)²).
What is A/x + B/(x+1) + C/(x+1)²?
When both sine and cosine powers are even, we first apply this type of identity.
What is a power-reduction identity?
The method used to evaluate∫ 1/√(4 − x²) dx.
Trig Substitution.
After substitution in ∫ sin(x)cos³(x) dx, the integral becomes this
What is ∫ u³ du?
The best method to evaluate ∫ x e^x dx.
What is integration by parts?
This method is used to evaluate ∫ (6−2x)/(x(x+1)²) dx.
What is Integration by Partial Fractions?
The identity used to rewrite sin²(x).
What is (1 − cos(2x))/2?
For∫ 5√(49 − x²) dx, the substitution for x is this.
What is x = 7sin(θ)?