Integrate <mrow> 9 <msqrt> tan −

Kevin Snyder

Kevin Snyder

Answered question

2022-05-13

Integrate 9 tan 1 ( 3 x ) 7 ( 9 x 2 + 1 ) with respect to x.

Answer & Explanation

Gerardo Barry

Gerardo Barry

Beginner2022-05-14Added 17 answers

Since 97 is constant with respect to x, move 97 out of the integral.

97tan-1(3x)9x2+1dx

Let u2=tan-1(3x). Then du2=39x2+1dx, so -du2=-39x2+1dx. Rewrite using u2 and du2.

9713u2du2

Since 13 is constant with respect to u2, move 13 out of the integral.

97(13u2du2)

Simplify the expression.

37u212du2

By the Power Rule, the integral of u212 with respect to u2 is 23u232.

37(23u232+C)

Simplify.

27u232+C

Replace all occurrences of u2 with tan-1(3x).

27tan-1(3x)32+C

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