Definite Integration: Substitution

Find the definite integral of 3x^2 * (x^3 + 2)^4 dx using the substitution method.

• (1/5)(x^3 + 2)^4 + C

• (1/4)(x^3 + 2)^5 + C

• (1/6)(x^3 + 2)^5 + C

• (1/5)(x^3 + 2)^5 + C

Evaluate the definite integral of (2x + 1) / sqrt(x^2 + x + 1) dx using the substitution method.

• 2√(x^2 + x + 1) + C

• 4√(x^2 + x + 1) + C

• √(x^2 + x + 1) + C

• 3√(x^2 + x + 1) + C

Calculate the definite integral of sin(2x) * cos(2x) dx using the substitution method.

• 2sin(2x)cos(2x) + C

• sin^2(4x) + C

• cos^2(4x) + C

• (1/4)sin^2(2x) + C

Determine the value of the definite integral of x * sqrt(4 - x^2) dx using the substitution method.

• (2/3)(4 - x^2)^(3/2) + C

• (2/3)(4 - x^2)^(1/2) + C

• (1/3)(4 - x^2)^(3/2) + C

• (2/3)(4 - x^2)^(2/3) + C

Find the definite integral of (x^2 + 1) / (x^3 + 3x) dx using the substitution method.

• ln|x^3 + 3x| + C

• ln|x^2 + 1| + C

• ln|x^3 + 1| + C

• ln|x^2 + 3x| + C

Evaluate the definite integral of e^(2x) / (e^x + 1)^2 dx using the substitution method.

• -1/(e^x + 1) + C

• -1/(e^x + 1)^2 + C

• -1/(e^x) + C

• -1/(e^(2x) + 1) + C

Calculate the definite integral of x * cos(x^2) dx using the substitution method.

• cos(x^2) + C

• (1/2) * sin(x^2) + C

• x * cos(x^2)

• x * sin(x^2) + C

Determine the value of the definite integral of (2x + 1) / (x^2 + x + 1) dx using the substitution method.

• ln|x^2 + x + 1| + C

• ln|x^2 + x + 1|^2 + C

• 2ln|x^2 + x + 1| + C

• ln|x^2 + x + 1| + x + C

Find the definite integral of x * ln(x) dx using the substitution method.

• 2ln(x) + C

• x * ln(x) + C

• x^2 * ln(x) + C

• (ln(x)^2)/2 + C

Evaluate the definite integral of (x^2 + 1) / (x^4 + 2x^2 + 1) dx using the substitution method.

• ln|sec(u) + tan(u)| + C

• ln|csc(u) + cot(u)| + C

• ln|tan(u) + sec(u)| + C

• ln|cos(u) + sin(u)| + C