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arbixerwoxottdrp1l

Answered question

2022-05-12

Evaluate 9 7 tan 1 ( x ) d x.

Answer & Explanation

Ellie Meyers

Ellie Meyers

Beginner2022-05-13Added 15 answers

Integrate by parts using the formula udv=uv-vdu, where u=tan-1(x) and dv=97.

tan-1(x)(97x)-97x1x2+1dx

Simplify.

tan-1(x)(9x)7-9x7(x2+1)dx

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

tan-1(x)(9x)7-(97xx2+1dx)

Let u=x2+1. Then du=2xdx, so 12du=xdx. Rewrite using u and du.

tan-1(x)(9x)7-971u12du

Simplify.

tan-1(x)(9x)7-9712udu

Since 12 is constant with respect to u, move 12 out of the integral.

tan-1(x)(9x)7-97(121udu)

Simplify.

tan-1(x)(9x)7-9141udu

The integral of 1u with respect to u is ln(|u|).

tan-1(x)(9x)7-914(ln(|u|)+C)

Rewrite tan-1(x)(9x)7-914(ln(|u|)+C) 97tan-1(x)x-914ln(|u|)+C.

97tan-1(x)x-914ln(|u|)+C

Replace all occurrences of u with x2+1.

97tan-1(x)x-914ln(|x2+1|)+C

Simplify.

18tan-1(x)x-9ln(|x2+1|)14+C

Reorder terms.

114(18tan-1(x)x-9ln(|x2+1|))+C

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