Practice your integration skills!

Apply the constant rule: ∫ k 𝑑 𝑥 = k 𝑥 .

Multiply: 5 𝑥

Add the constant of integration, 𝐶

The final answer is 5 𝑥 + 𝐶

Use the power rule

Apply 𝑛 = 3 to get (𝑥^4)/4

Add the constant of integration, 𝐶.

The final answer is (𝑥^4)/4 + 𝐶

Use the power rule

Apply 𝑛 = 5 to get (𝑥^6)/6 ​ .

Multiply 4 by 1/6 to get (4/6)(𝑥^6)

The final answer is (2/3)(𝑥^6) + 𝐶

Use the sum rule: Integrate each term separately.

Integrate 7𝑥^2 using the power rule: (7𝑥^3)/3 ​ .

Integrate 3x: (3𝑥^2)/2 ​

The final answer is (7𝑥^3)/3 + (3𝑥^2)/2 + 𝐶

Use the sum and difference rule to integrate separately.

Apply the power rule: 6𝑥^5/5 and −2𝑥^2/2

Simplify to get 6𝑥^5/5 - 𝑥^2.

The final answer is 6𝑥^5/5 - 𝑥^2 + C.

Use the sum rule: Integrate each term separately

Apply the power rule: 9𝑥^4/4 and 4𝑥^3/3

Write the result: 9/4(𝑥^4) + 4/3(𝑥^3)

The final answer is 9/4(𝑥^4) + 4/3(𝑥^3+ 𝐶

Use the sum rule: Integrate each term separately.

Apply the power rule: 2𝑥^6/6 and −3𝑥^3/3

Simplify: 1/3𝑥^6 − 𝑥^3/3

The final answer is 1/3𝑥^6 − 𝑥^3/3 +C.

Integrate 5𝑥^2 to get 5𝑥^3/3

Integrate 2𝑥 to get 𝑥^2.

Integrate −1 to get −𝑥

The final answer is (5/3)𝑥^3 + 𝑥^2 − 𝑥 + 𝐶

Integrate 8𝑥^3 to get 8𝑥^4/4

Integrate −2𝑥 get −2𝑥^2/2

Simplify to get 2𝑥^4 − 𝑥^2

The final answer is 2𝑥^4 − 𝑥^2 + C.

Use the sum rule: Integrate each term separately.

Apply the power rule: 3𝑥^7/7 and 4𝑥^2/2

Write the result: 3𝑥^7/7 and 2𝑥^2

The final answer is 3𝑥^7/7 and 2𝑥^2 + C.