Compute ∫0−2x3+4x2+7x−20x2+4x+8dx+∫202x3−7x2+9x−10x2+4dx
Compute ∫π02xsinx3+cos2xdx
Given that the value ln(2) is not the root of any polynomial with rational coefficients. For any nonnegative integer n, let pn(x) be the unique polynomial with integer coefficients such that pn(ln(2))=∫21(ln(x))ndx
Compute the value of the ∞∑n=01pn(0)
The set of points (x,y) in the plane satisfying x2/5+|y|=1 form a curve enclosing a region.
Compute the area of this region.
Compute the value of ∫20√4−xx−√x4−xdx
Find the value of I=∫e−sinxsin(2x)(1−sinx)2dx
Let f(x)={cosx,x∈[−π2,0)ex,x∈[0,1]
Compute ∫1−π2f(x)dx.
Compute ∫1sinxdx
Compute ∫π401sinx+cosxdx
Compute ∫1ax+bdx
Compute ∫1x2−axdx
Compute ∫1√a2−x2dx
Compute ∫x1+x2dx
Compute ∫lnxxdx
Compute ∫sin5xdx
Compute ∫secxdx
Compute ∫secxdx
Compute ∫1√x2+1dx
Compute ∫1√x2+4x+5dx
Compute ∫x3lnxdx
Compute ∫arctanxdx
Evaluate ∫eaxcos(bx)dxand∫eaxsin(bx)dx
Evaluate ∫x2exdx
Evaluate ∫x2sinxdx
Compute ∫√x2+a2dx