The Combine command combines integrals using linearity.

The parameter v is any expression involving definite or indefinite integrals. Definite integrals will have their variable of integration renamed to facilitate combination.

For indefinite integrals, this command is equivalent to calling combine(v, int).

$\mathrm{with}\left(\mathrm{IntegrationTools}\right)\:$

$v≔\mathrm{Int}\left(af\left(x\right)+bg\left(x\right)+ch\left(x\right)\,x=1..2\right)$

$v≔{\int }_1^2\left(af\left(x\right)+bg\left(x\right)+ch\left(x\right)\right)\ⅆx$

$w≔\mathrm{Expand}\left(v\right)$

$w≔a\left({\int }_1^{2}f\left(x\right)\ⅆx\right)+b\left({\int }_1^{2}g\left(x\right)\ⅆx\right)+c\left({\int }_1^{2}h\left(x\right)\ⅆx\right)$

$\mathrm{Combine}\left(w\right)$

${\int }_1^2\left(af\left(x\right)+bg\left(x\right)+ch\left(x\right)\right)\ⅆx$

$\mathrm{Combine}\left(\mathrm{Int}\left(f\left(x\right)\,x=a..b\right)+\mathrm{Int}\left(f\left(y\right)\,y=b..c\right)-\mathrm{Int}\left(f\left(z\right)\,z=a..d\right)\right)$

${\int }_d^{c}f\left(x\right)\ⅆx$

$\mathrm{Combine}\left(\mathrm{Int}\left(f\left(x\right)\,x\right)+\mathrm{Int}\left(g\left(x\right)\,x\right)\right)$

$\int \left(f\left(x\right)+g\left(x\right)\right)\ⅆx$