Inclusion Criteria:

          1. Women ≥ 18 years old with a diagnosis of primary, recurrent or progressive uterine,
             ovarian, fallopian tube or peritoneal carcinosarcoma, for whom treatment with
             combination paclitaxel and carboplatin is recommended.

          2. Written informed consent/assent prior to any study-specific procedures

          3. Eastern Cooperative Oncology Group (ECOG) performance status 0-2

          4. Tissue available for translational study (paraffin block or new biopsy) .

          5. Adequate bone marrow, renal, and hepatic function as defined per protocol.

          6. No disease-modifying therapy, including investigational treatments, within 28 days
             prior to initiation of study treatment.

          7. Ability to swallow tablets

          8. For Women of child-bearing potential:Willingness to use a highly effective method of
             contraception during the study and for 6 months following the last dose of
             galunisertib. Negative beta human chorionic gonadotropin pregnancy test documented
             within 7 days prior to initiation of study drug.

          9. Patient must have measurable disease before the treatment

        Exclusion Criteria:

          1. Planned radiotherapy during or after the study chemotherapy prior to disease
             progression.

          2. Receipt of chemotherapy or radiation within 28 days of study treatment

          3. Have had a major surgical procedure or a significant traumatic injury within 28 days
             prior to study treatment; Minor procedures such as biopsy within 7 days prior to study
             treatment are allowed.

          4. Active infection that would preclude receipt of chemotherapy

          5. Moderate or severe cardiovascular disease per protocol

          6. Active pregnancy or lactation

          7. Second primary malignancy for which treatment during the study period would be
             recommended if this cancer were not also present.

          8. Prior malignancy requiring treatment within the last 3 years

          9. Use of another investigational product or device within 4 weeks of study entry or
             during study participation.