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In this lesson, we will learn how to find the antiderivative of a given function.

Q1:

Find the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = ( π₯ β 3 ) 2 .

Q2:

Determine the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = 6 π₯ + 7 π₯ 1 5 2 5 β .

Q3:

Find, if possible, an antiderivative πΉ of π ( π₯ ) = 1 2 π₯ β 1 that satisfies the conditions πΉ ( 0 ) = 1 and πΉ ( 1 ) = β 1 .

Q4:

Determine the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = β 2 π 2 .

Q5:

If π β² β² ( π₯ ) = 3 π₯ + 3 π₯ + 5 π₯ + 2 5 3 , determine π ( π₯ ) .

Q6:

Determine the most general antiderivative πΉ ( π₯ ) of the function π , given that π ( π₯ ) = 5 2 + 4 π₯ .

Q7:

Determine the antiderivative πΉ of the function π ( π₯ ) = 5 π₯ + 4 π₯ 4 3 where πΉ ( 1 ) = β 2 .

Q8:

Find the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = 2 π₯ β 3 π₯ β π₯ 7 5 2 .

Q9:

Find the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = 4 π₯ β 2 .

Q10:

Find the antiderivative of the function π ( π₯ ) = 2 π₯ + 3 π₯ + 3 2 .

Q11:

Determine the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = β π₯ + 5 β π₯ 3 .

Q12:

Determine the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = 4 π₯ ( β π₯ + 5 ) .

Q13:

By considering the product rule, find a function π so that π β² ( π₯ ) = π β π₯ + 2 π β π₯ π₯ π₯ .

Q14:

Determine the most general antiderivative πΉ ( π₯ ) of the function π if π ( π₯ ) = β 2 π₯ + π₯ β 2 π₯ 2 π₯ 4 3 3 and π₯ > 0 .

Q15:

Find the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = 2 5 π₯ + 2 9 5 π₯ + 5 2 2 .

Q16:

Find the most general antiderivative of the function π ( π₯ ) = 4 π₯ + 3 β 2 3 β π₯ s i n .

Q17:

What is the antiderivative πΉ of π ( π₯ ) = β 5 + οΉ 1 + π₯ ο 2 β 1 that satisfies πΉ ( 1 ) = 0 ?

Q18:

Find the most general antiderivative πΊ ( π‘ ) of the function π ( π‘ ) = β 3 π‘ + 5 π‘ + 4 4 β π‘ ο¨ .

Q19:

Find the most general antiderivative πΊ ( π‘ ) of the function π ( π‘ ) = π‘ β 4 π‘ + 5 β π‘ ο¨ .

Q20:

Determine the most general antiderivative πΉ ( π₯ ) of the function π ( π₯ ) = β 2 β π₯ + 3 π₯ β π₯ 3 2 .

Q21:

Determine the most general antiderivative of the function π ( π ) = β 3 π + 2 π π π t a n s e c .

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