Integrate the following functions. ∫x21−x6dx.
∫x21−x6dx Let I=∫x21−x6dx=∫x21−(x3)2dx Let x3=t⇒3x2=dtdx⇒dx=dt3x2 ∴I=∫x21−t2dt3x2=13∫dt1−t2=13.12log∣∣1+t1−t∣∣+C[∵∫dxa2−x2=12alog∣∣a+xa−x∣∣]=16log∣∣1+x31−x3∣∣+C(∵t=x3)
Integrate the following functions. ∫x2√x6+a6dx.
Integrate the following functions. ∫1√x2+2x+2dx.
Integrate the following functions. ∫1√(2−x)2+1dx.