Latihan Matematika Wajib Kelas XI Integral Substitusi
# 9
Pilgan

x2(x3+3)5dx= ....\int x^2\left(x^3+3\right)^5dx=\ ....

A

118(x3+3)5+C\frac{1}{18}\left(x^3+3\right)^5+C

B

118(x3+3)6+C\frac{1}{18}\left(x^3+3\right)^6+C

C

2x(x3+3)6+C2x\left(x^3+3\right)^6+C

D

x2(x3+3)6+Cx^2\left(x^3+3\right)^6+C

E

12(x3+3)6+C\frac{1}{2}\left(x^3+3\right)^6+C

Pembahasan:

Misalkan u=x3+3u=x^3+3, maka du=3x2dxdu=3x^2dx dx=du3x2\Leftrightarrow dx=\frac{du}{3x^2}

Sehingga menjadi:

x2(x3+3)5dx=(x3+3)5x2dx\int x^2\left(x^3+3\right)^5dx=\int\left(x^3+3\right)^5x^2dx

=u5x2du3x2=\int u^5x^2\frac{du}{3x^2}

=u5du3=\int u^5\frac{du}{3}

=13u5du=\frac{1}{3}\int u^5du

=13(15+1u5+1)+C=\frac{1}{3}\left(\frac{1}{5+1}u^{5+1}\right)+C

=13(16u6)+C=\frac{1}{3}\left(\frac{1}{6}u^6\right)+C

=118u6+C=\frac{1}{18}u^6+C

=118(x3+3)6+C=\frac{1}{18}\left(x^3+3\right)^6+C


Jadi, hasil integral substitusi tersebut adalah 118(x3+3)6+C\frac{1}{18}\left(x^3+3\right)^6+C