Aku n MATEMATIKA cah SMA Nda: PR SEKOLAH

No - 1

$\dpi{100} \fn_cs \int (6x^{2}-\frac{1}{x}+3).dx=....$

JAWAB :

$\dpi{100} \fn_cs =2x^{3}-ln\left | x \right |+3x+C$

No - 02

$\dpi{100} \fn_cs \int x.(x-4)^{2}.dx=....$

JAWAB :

karena pangkatnya masih 2 jadi kita uraikan saja menjadi
$\dpi{100} \fn_cs =\int x.(x^{2}-8x+16).dx=\int (x^{3}-8x^{2}+16x).dx$
$\dpi{100} \fn_cs =\frac{1}{4}x^{4}-\frac{8}{3}x^{3}+8x^{2}+C$

No - 03

$\dpi{100} \fn_cs \int (\frac{cos\, 2x}{10}+\frac{sin\, 3x}{5}).dx=$

JAWAB :

$\dpi{100} \fn_cs =\frac{sin\, 2x}{20}-\frac{cos\, 3x}{15}+C$

No - 04

$\dpi{100} \fn_cs \int (1-ctg\, x).(1+ctg\, x).dx=....$

JAWAB :

$\dpi{100} \fn_cs =\int (1-ctg\, x).(1+ctg\, x).dx=\int (1-{\color{Red} ctg^{2}\, x}).dx$
$\dpi{100} \fn_cs =\int (1-{\color{Red} (cosec^{2}\, x-1)}).dx=\int (2-cosec^{2}\, x).dx$
$\dpi{100} \fn_cs =2x+cotg\, x+C$

No - 05