Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)7\sin^{8}(x)\cos(x)\ln(\sin(x))dxno. 101. \int u^{n}\ln u du=\frac{u^{n+1}{(n+1)^{2}}[(n+1)\ln u-1]+C

pancha3

pancha3

Answered question

2021-05-17

Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
7sin8(x)cos(x)ln(sin(x))dx

no. 101. unlnudu=un+1(n+1)2[(n+1)lnu1]+C

Answer & Explanation

Obiajulu

Obiajulu

Skilled2021-05-18Added 98 answers

Step 1
Integral: =7(sin8x)cosxln(sinx)dx
Let us sinx=u
cosxdx=du
Substituting it in integral
Integral: =7u8lnudu
In table of Integral it is in born of integral no. 101. unmudu=Un+1(n+1)2[(n+1)lnu1]+c
n=8 Integral: =7[u8+1(8+1)2[(811)mu1]]+c
=7u981[9mu1]+c
=7sin9x81[9m(sinx)1]+c

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