Pazopanib Hydrochloride, Paclitaxel, and Carboplatin in Treating Patients With Refractory or Resistant Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Peritoneal Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or peritoneal carcinoma * Recurrent disease * Received at least 1 prior platinum treatment and developed platinum-refractory disease (i.e., progression within 4 weeks of platinum administration) or platinum-resistant disease (i.e., progression within 6 months after the last platinum dose) * There is no restriction on the number of prior lines of treatment * Non-platinum treatment is allowed after proven platinum-resistance or -refractory disease * Evaluable (measurable or nonmeasurable) disease according to RECIST version 1.1 criteria * Patients with refractory disease on weekly paclitaxel and carboplatin regimen are excluded (phase II only) * No known gastrointestinal intraluminal metastatic lesions with risk of bleeding * No known endobronchial lesions and/or lesions infiltrating major pulmonary vessels * No known brain metastases or leptomeningeal disease PATIENT CHARACTERISTICS: * WHO performance status 0-2 * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Hemoglobin ≥ 9 g/dL * Platelet count ≥ 100 x 10\^9/L * PT, aPTT, or INR ≤ 1.2 times upper limit of normal (ULN) * Total bilirubin ≤ 1.5 times ULN\* * ALT and AST ≤ 2.5 times ULN\* * Serum creatinine ≤ 1.5 mg/dL OR calculated creatinine clearance ≥ 50 mL/min * Urine protein creatinine ratio \< 1 OR 24-hour urine protein \< 1 g * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during study therapy * No other prior primary or recurrent malignancies treated within the past 2 years except for completely resected non-melanomatous skin carcinoma or successfully treated carcinoma in situ of the skin or uterine cervix * No known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs similar or related to paclitaxel, carboplatin, and pazopanib hydrochloride * Able to receive infusions of paclitaxel and carboplatin * Able to swallow pazopanib hydrochloride tablets * No unstable or serious condition (e.g., uncontrolled infection requiring systemic therapy) * No history of any of the following cardiovascular conditions within the past 6 months: * Myocardial infarction * Unstable angina * Symptomatic peripheral vascular disease * NYHA class III-IV congestive heart failure * LVEF \> 50% as assessed by ultrasound or MUGA scan, if clinically indicated * No inadequately controlled hypertension (SBP ≥ 140 mm Hg or DBP ≥ 90 mm Hg) * Initiation or adjustment of blood pressure medication is permitted prior to the study entry * No prolonged corrected QT interval (QTc) defined as \> 480 msecs using Bazett formula * No history of cerebrovascular accident within the past 6 months, including any of the following: * Transient ischemic attack * Pulmonary embolism * Untreated deep venous thrombosis (DVT) * Patients with recent DVT who have been treated with therapeutic anti-coagulating agents for at least 6 weeks are eligible * No evidence of active bleeding or bleeding diathesis * No clinically significant gastrointestinal (GI) tract abnormalities that may increase the risk for GI bleeding including, but not limited to, any of the following: * Active peptic ulcer disease * Inflammatory bowel disease (e.g., ulcerative colitis or Crohn disease) * No history of bowel obstruction (excluding postoperative (i.e. within 4 weeks post surgery)) during the whole prior history of the patient, or other GI condition with increased risk of perforation such as clear infiltration into the rectosigmoid, colon or small bowel. * No clinically significant GI abnormalities that may affect absorption of investigational product including, but not limited to, any of the following: * Malabsorption syndrome * Major resection of stomach or small bowel * No hemoptysis in excess of 2.5 mL (one-half teaspoon) within 8 weeks prior to first dose of study drug * No psychological, familial, sociological, or geographical condition potentially hampering compliance with the study protocol and follow-up schedule * No trauma within the past 28 days * No prior non-healing wounds, fracture, or ulcer PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No ongoing toxicity from prior anticancer therapy \> grade 1 and/or that is progressing in severity, except for alopecia and ≤ grade 2 peripheral neuropathy * No cardiac angioplasty or stenting within the past 6 months * No coronary artery bypass graft surgery within the past 6 months * At least 14 days since prior radiotherapy, surgery, or tumor embolization , chemotherapy, immunotherapy, biologic therapy, investigational therapy, or hormonal therapy (28 days for drugs with a longer half-life) * At least 14 days since prior (28 days for drugs with a longer half-life) and no concurrent prohibited medications * At least 28 days since prior major surgery (procedures such as catheter placement and diagnostic endoscopic procedures are not considered to be major)