Integration by Trigonometric Substitution

Front

Identify the appropriate trigonometric substitution for the integral: ∫(x^2)√(4-x^2) dx

Back

x = 2sin(t)

Front

Recognize when to use trigonometric substitution for the integral: ∫(x^3)√(1-x^2) dx

Back

Trigonometric substitution should be used for the integral ∫(x^3)√(1-x^2) dx.

Front

Apply trigonometric substitution to simplify the integral: ∫(x^2) / √(4+x^2) dx

Back

2 * (θ + tan(θ) * sec(θ)) + C

Front

Trigonometric substitution for ∫(x^3) / (1+x^2) dx

Back

x = tan(theta)

Front

Recognize the correct trigonometric substitution for the integral: ∫(x^2) / (1+x^2) dx

Back

x = tan(theta)

Front

Apply trigonometric substitution to simplify the integral: ∫(x^3) / √(9-x^2) dx

Back

-6√(9-x^2) + C

Front

Identify the appropriate trigonometric substitution for the integral: ∫(x^2) / (1-x^2) dx

Back

x = sin(theta)

Front

Recognize when to use trigonometric substitution for the integral: ∫(x^3) / (1-x^2) dx

Back

Trigonometric substitution

Front

Apply trigonometric substitution to simplify the integral: ∫(x^2) / √(1+x^2) dx

Back

(1/2) * (sqrt(1+x^2) * (x^2 - 1) + ln(abs(x + sqrt(1+x^2)))) + C

Front

Trigonometric substitution for ∫(x^3) / (1-x^2) dx

Back

x = sin(theta)