CalculusAdditional / Further Maths

Integrating exponentials

Integrate natural exponentials with linear exponents.

  • . A constant multiplier stays in front.
  • for .
  • Keep the exponent unchanged and divide by its derivative.

Example 1

Integrate with respect to .

Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.

Example 2

Integrate with respect to .

Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.

Your turn

Question 1

Integrate with respect to .

Check answer
Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.
Question 2

Integrate with respect to .

Check answer
Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.
Question 3

Integrate with respect to .

Check answer
Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.
Question 4

Integrate with respect to .

Check answer
Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.
Question 5

Integrate with respect to .

Check answer
Find the inner derivative.The exponential keeps the same exponent. Divide by the inner derivative.
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